Frames
Your riding style, or rather the intended use, for the unicycle determines the things to look out for.
Freestyle
I'm now freestyle whizz so I'm not going to write too much about what makes a really good freestyle frame but it's safe to say that one with a flat as opposed to rounded crown is the one to look out for. The flat crown gives you a good resting place to put one of your feet for one footed tricks. Miyata unicycles are very common and very well liked amongst freestyle riders. The most popular size for a freestyle unicycle is a 20" although some taller riders sometimes prefer a 24".
MUni (Mountain Unicycling)
Taking your unicycle off road or downhill places a lot of strain on just about all parts. The frame is no exception. You'll want one that's strong and, if you can afford the extra money, as light as possible. The lightness is desirable due to the fact that a MUni frame will invariably have a 26" (sometimes a 24" through personal choice) wheel which is in itself very heavy so saving any extra weight on the frame is a real bonus. Another thing to pay particular attention to is the width of the forks - ideally you want to get a 3" wide tyre in there as this really helps soak up the bumps and drops along the way.
Trials / Urban
2 sizes or frame are common for this style of riding: 20" and 24". The later is only really common due to the fact (at the time of writing and this will change) you can get the stronger splined hubs and cranks of the right length capable of taking the abuse. If prefer the 20" for trials as it's lighter for all the jumping around you do but I'm forever bending cranks. Anyway... back to frames! For trials you want a big fat bouncy tyre so your frame needs to be wide enough to accommodate a 2.5" or wider tyre like the Monty rear bike trials one. For said Monty tyre there are only a few true 20" frames I know of that will fit said tyre: KH20, Sem and United from Unicycle.com US and the Nimbus II from Unicycle.com UK . Other than that you can go for a 24" frame which *should* be wide enough but it's worth checking to make sure. If you're going for a 24" setup then you'll want a frame wide enough for a 3" tyre so may well end up having to go for a 26" or 28" frame.
It's always worth checking the your intended frame will fit on the hub of your wheel. The higher end trials and MUni frames are mostly designed for high end hubs like the Profile which are generally wider than standard cheap cotterless ones.
Bearing Holders
There are 2 main tyres of bearing holders:
Lollipop
These are normally found on cheap Taiwanese unicycles and should generally be avoided. A lollipop bearing housing consists of a cast metal disc in to which the bearings are inserted. Coming off said disk is a plug that get inserted directly into the bottom ands of the fork and are held in place usually by 2 bolts passing straight through the fork and bearing housing. This make it a real pain if you want to take the wheel off to change the tyre. They also cause a well known problem in that they will split the fork tubing if you show them any amount of abuse. The one exception to this rule seems to be those found on the Pashley MUni. I've never heard of anyone having this same problem.
Split
Split bearing housings consist of 2 cups that are held round the bearing by 2 bolts. One of the cups is welded to the end of the frame fork. These are accepted as being a much better design than the lollipop housing for 2 reasons: you won't split your fork tubing and they make it a lot easier to take the wheel off. Higher end unicycles will have precision machined bearing housings that hold the bearings much better than the cheaper (and lighter) pressed steel variety. You have to take care not to over tighten this style of bearing housing otherwise you'll squash the bearings themselves.
Bearings
Over time dirt and water can work their way in to the bearings and lubricant work its way out resulting in all sorts of creaking and groaning noises as you ride along and the wheel taking more force to actually turn. For this reason it's worth investing in a good set of sealed bearings. When looking at bearings lookout for the following codes from worst to best (many thanks to Roger Davies of Unicycle Source UK for these):
A word from Roger, "Personally I would only consider -2rs as they help keep moister out - but I do live in the UK! For most inside things -zz are OK. I would never consider using any of the others."
Axles / Hubs
For me the hub is one of the most important parts of the unicycle. The main reason for this is that fact that the type of hub you have directly affects the tyre of cranks you can put on it: tapered or splined. The later being the strongest and least likely to bend or break. There are three types of hub you are likely to come across:
Cottered
These were common on older unicycles and are now almost a thing of the past. They can be spotted by the fact that the crank has a bolt passing directly though it and holding it in place on the hub. These are pretty weak and should generally be avoided.
Cotterless
These are by far the most common hub you'll find on a unicycle and are well suited to normal riding styles. You can spot this kind of hub as they have a square taper at either end to mount the cranks on. Cheaper Taiwanese unicycles tend to have low end cotterless hubs which can be broken if you treat them rough enough e.g. dropping off stuff higher than a curb for instance although your cranks will probably bend first. It is generally accepted that the Suzue hub used in Miyata unicycles is the best of this kind and is unlikely to break unless you really go big.
Splined
These are the high end hubs. Precision engineered, very strong and incredibly hard to break no matter what you throw at them. These hubs are bullet-proof and the splined cranks the take are much stronger and far less likely to bend. If you are going to do trials and / or MUni and plan on doing lots of drops over the 2' range then I'd strongly recommend a splined hub.
Cranks
Jumping on, off and over obstacles places great amounts of strain on your cranks as they take most of the impact when you land. Ask anyone who drops of things higher than a curb with any regularity and they'll tell you about bent cranks! Even with the best landing technique in the world - if you take a high drop on duff cranks they're going to bend. For each of the 3 types of hub above each take their own specific type of crank: cottered take cottered, cotterless take taper fit and splined take splined cranks. If you're regularly planning on doing drops over 1' then I'd highly recommend spending the extra cash to get a splined hub and cranks - you'll save yourself a lot of frustration and time spent replacing bent cranks if you do.
Cranks come in a multitude of different lengths and each are suited to slightly different riding styles. Take the following as merely a guide and not gospel:
20" Wheels
For freestyle 125mm cranks are good as they give a reasonable amount of control and keep you moving along at a good rate. However, for trials riding you really want some extra control so longer cranks in the range of 135-145mm are usually preferred. cotterless cranks are hard to find in this length range though. Lasco do make 140mm cranks but these are best avoided as they are known to bend and break (at the time of writing anyway) without much help. PRofile do make 145mm splined cranks to go on their excellent splined hub. I have a set of these on my 20" trials uni and they are as straight and true as the day I got them :-)
24" Wheels
Anything in the range of 125-170mm cranks can be used. The shorter they are the faster you'll go but have less control than with longer ones. It's up to you what you want your 24" to do - for distance riding shorter cranks but for tricks you'll want the longer ones. For MUni or trials riding it's definitely a case of the longer the better.
26" Wheels
These are generally the preserve of MUni riders although they will make a relatively good commuting unicycle. 170-175mm cranks are highly advised for MUni as the extra torque they give you helps get up and over obstacles. However, if you're looking for a road machine then 150mm cranks (or even short if you dare) would be better for you.
Over 26" Wheels
I haven't done a huge amount of riding on bigger wheels so I'm not going to really comment on cranks lengths for these. Speed demons like Roger Davies use 110mm cranks on 36" Cokers and produce some amazing speeds! Most mortals work with 150-160mm cranks for similarly sized wheels though.
Pedals
Pedals come in 2 sizes 1/2" and 9/16" with the size corresponding to the thickness of the axle that screws in to your cranks. 9/16" are the most common these days.
You'll see a big jump in prices for pedals. The reason for this is the higher end pedals have sealed bearings to stop dirt getting in an lubricating grease getting out.
For indoor riding you'll need to have plastic pedals so you don't scratch up the nice and shiny gym floor. Plastic can also be used outdoors of course but I've yet to find a set that offer any where near the same grip that can be found with the metal varieties.
By far the most common metal ones are platform pedals. These all have a large area for your foot with a series of metal studs screwed in to both sides for added grip.
You also get what are known as "caged" pedals. These have a single or sometimes a double set of spiked metal cages. While cadged pedals offer great amounts of grip they also pose a real danger to your shins. I've had so many gouges taken out of my legs from this style of pedal that I invariably wear some kind of shin guard when I'm jumping around.
For ultimate grip I find metal platform pedals with screw in studs (Easton "Cully" and Atomlab "Aircorp" to name but a few) to fit the bill. One thing to watch out for with these style of pedals is the thickness of the pins. If you are riding trials and pedal grabbing the thinner M3 (3mm thick) pins get bent flat against the pedal body and stop being quite so grippy. If this is an issue for you then look for ones with M4 (4mm thick) pins such as the Aircorp. The extra 1mm of thickness makes a surprising difference.
Rims
Your choice of rim is only really important for high stress riding like MUni and trials where your wheel comes in for some real punishment. Double wall aluminium rims are both lighter and usually stronger than the single walled steel rims you find on lower end unicycle wheels. Keep in mind that if you're looking at having a big fat tyre on your unicycle you'll also need a big fat rim like the Sun "DoubleWide", Zum "Eliminator",Halo "Combat" rims or the 20" Monty specific rear wheel rim.
For Muni you might want to run a brake on your uni. This will influence your choice of rim as,ideally, you want one with a braking surface. The braking surface is basically a bare metal area running round the rim for brake pads to grip against. Brakes will work with other painted rims without the braking surface but the stopping power is reduced and it'll make a lot of noise!
Tyres
For riding indoors you'll need a non marking tyre otherwise you'll let everyone see exactly where you've been riding. For any kind of outdoor riding get as fat a tyre as your rim and frame can handle. These soak up lumps and bumps and are more stable than the thinner variety. You'll find a selection of all sorts of tyres here .
The pressure you run a tyre at (how much air you pump in there) affects your riding to quite some degree. Higher pressures give you a solid tyre with a low rolling resistance that makes turning a lot easier as there is less rubber in contact with the riding surface. Lower pressures (15-25 PSI) mean more of the tyre touches the ground resulting in increased grip and adding some shock absorbtion when riding over small bumps, tree roots, stones and the like. Hopping and jump is also a lot easier with lower pressure as you get a good deal of extra spring from the tyre.
For MUni and trials riding where you are hopping and dropping off things and crossing rougher terrain low tyre pressure is a real bonus but you have to watch out - too little pressure in the tyre and when you land a drop off something your tyre can "bottom out" and the force of the landing pushes the rim down and makes contact with the ground. Tyres with thick side walls help here as you can run them at lower pressure but, because of the thicker, stronger side wall you are less likely to bottom out on your rim.
Another common problem when hopping and jumping around can be the tyre folding off the rim when you land side on. This is exagerated as the pressure in the tyre goes down - said pressure helps push the bead of the tyre (the inner edge of the tyre that hooks in to the rim) against the rim and keep it in place. Different tyres have beads and the more aggressive tyres have bigger and better beads to reduce the chances of this ever happening. The same can be said for rims - higher end rims have had plenty R & D go in to how they hang on to the tyre under stressful rinding conditions. Some are better than others!
Seats
Unicycle seats have a long way to go yet. Comfort doesn't really come in to any of the off the shelf seats available and riders are forced to resort to customising their seats in to what are commonly known as "air seat" by removing the cover and inserting an inner tube from a tyre.
The only seat I'd really recommend is the Miyata. While it's the most comfy of the stock seats I've ever tried, all of mine have been converted in to air seats. The Miyata also comes with a handle at the front which is invaluable for hopping and jumping.
One of the most common seats other than the Miyata is the "Viscount". These tend to vary from feeling like a brick to quite comfortable. They are, however, also known for the bumpers falling off which ain't so hot!
Cheap unicycles (some more expensive ones too!) come with really bad seats that feel like you're riding and sitting directly on the seat post. If you want to ride for more than 5 minutes at a time you'll need to get a better seat for sure.
A word on air seats... if you're riding with any regularity you'll likely come to realise that your seat could be a lot more comfortable. Enter the air seat! These are basically a stock seat with the cover removed and a small (12-20") inner tube inserted and the cover replaced. The inner tube is then inflated an provides much greater padding / cushioning for your rear end. Miyata saddles are by far the easiest to convert but Viscounts can be "done" as well.
If you want to get extreme with your seat you can go the whole way and get one with a carbon fiber seat base (light weight, rigid and near indestructible), an inner tube for padding and a large seat cover such as the Roach or Gemcrest. Thanks to the nature of the carbon seat base it can be drilled to take virtually any seat post and handle. the only rear bumper i know of that will fit it is the Miyata though.
I mention handles for your seat. For a long time only Miyata saddles had a small plastic handle on the front. These were a real boost for MUni and trials riding where you use it to pull up on the unicycle for hopping, jumping and going up and down steep hills. Howeer, the design could be better. They are kind of small for a large adult hand to grip and problems with finger pain after long periods of use are common. Chris Reeder in the USA decided to do something about this and started developing a new handle. Head to Unicycle.com and search for a "Reeder Handle" and you'll see what they look like. They are a vast improvement and offer a much bigger grip to get your fingers round. They are, however, left or right hand specific. There is a reason for this though - the are angled so that, when holding the handle, your forearm is straight and not twisted as it would be with a Miyata style handle. This helps reduce the stress and strain on your arm, wrist and fingers and so ruduce the chances of any pain after excessive amount of hopping. Big thanks to Chris for taking the time to develop these!!!
Seat Post Clamps
On cheap unicycles you can find that the seat will twist left or right when you are out riding. This is mainly due to a poor fitting seat post clamp - it just won't tighten enough to grip the seat post well enough to stop this happening.
Quick Release
Low end unis generally have ineffective quick releases that are difficult to clamp down tight enough to prevent the seat from moving.
Double Bolt
If you are not going to move your seat height then the best about are the double bolt BMX clamps. They are a pain at workshops.
