A unicycle is built around the frame, so let’s start there.
FRAME:
The Wyganowski is, I think, the only frame out there that’s actually made with Freestyle in mind:
http://www.unicycle.com/shopping/shopexd.asp?id=82
That’s the 48-spoke version, there is also a 36.
For a Freestyle frame, there are four major considerations, which I think are important in this order:
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20" frame (if you’re using 20" wheel)! If you have a 2" gap above your tire, anything involving coasting, gliding, stand-up skills, will range from more difficult to nearly impossible.
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Foot platform: Bigger is generally better. The Wyganowski, Sem XL, Miyata Standard and similar fork crowns offer better foot support than the Miyata Deluxe, for instance.
The KH frames are made for seated one-footing, coasting, and gliding, but not for stand-up and other skills where you want a flat crown.
In my mind, the ultimate Freestyle frame is yet to be made. Someday I may experiment with a foot plate on the fork to improve foot support. This will be a challenge though, because you have to leave room for wheel walking and other skills, so the final result has to be a compromise.
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Strength: Some Freestyle skills put forces on the frame at odd angles. The one and only new trick I used in 1994, the last time I did a Freestyle competition, eventually broke my frame. I had to compete on a borrowed one.
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No protrusions: A Miyata frame, for instance, has a seat post clamp that’s welded on, and the bolt can cut up your legs. I dealt with this for years before finally getting a custom frame built with the clamp way up at the top. With a removeable clamp you will have more options.
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(In case you want a fatter tire) Tire clearance: I like the Primo The Wall tires for Freestyle. They fit perfectly in my Wyganowski frame. But if you want to use a wider tire, make sure your frame will fit it. Most Freestyle frames are just wide enough for the Primo.
Pedals:
If you’re riding indoors, they have to have plastic ends. This is also true if you intend to compete, because metal pedals are not likely to be allowed in the gym. Semcycle used to have the best Freestyle pedals, but the manufacturer (Sakae?) stopped making them many years ago. They were similar to these pedals:
http://www.unicycle.com/shopping/shopexd.asp?id=217
but had a square cross section, not concave. But those United pedals are also very good, as well as cheap!
Most of the pedals on Unicycle.com are metal, therefore not good for indoors. If you never ride indoors, a grippy metal pedal will be okay, but will occasionally eat your legs. So I recommend plastic.
My favorite pedals at the moment are from MYS, that crazy Japanese Web site connected with the Japan Unicycling Association:
http://www.mys-co.com/newSite/shopping/cgi-bin/shop.cgi?lang=eng
They are the first pedal listed on the pedals page. Soft rubber ends and very grippy! But I have no experience ordering from that site, so you’re on your own if you order those. I bought mine from Daiki Izumeda at UNICON.
WHEEL:
You want it not to break, of course, while also not too heavy. But if you’re serious about Freestyle, strength is probably more important than lightness. 36 spokes is the common number, keeping your cost down and giving you more choice of parts. it should be plenty for most Freestyle applications.
But if you do stuff with the unicycle laying on its side, standing on it, swinging it around, those extra spokes are going to make a difference.
Rims aren’t as much of an issue as with larger wheels. A 20" wheel tends to be pretty strong because it’s not so big. As long as you don’t get cheap with your rim you should be fine.
AXLE:
Splined is probably overkill for Freestyle. Though I used to break a lot of axles, I was using the cycle for a combination of things, many of which will now be done by other unicycles that have come along since, like my Trials uni. If you use a splined axle you have very imited choices on cranks, and they are generally going to be both too long and too wide.
The old Semcycle axles were easily the strongest available, but today’s Sem axle is about equal to the Suzue. Both are good, and the Suzue costs less. Make sure the bearing width matches your frame.
CRANKS:
Freestyle cranks will bend if you do lots of hopping, so don’t be cheap here either. The main question is length. At Unicycle.com, the Bicycle Euro and Dotek ones look good, but I don’t know the strength on them.
For Freestyle, 140mm is generally considered too long. I rode for many years with 125mm, which is also considered long by today’s standards. Right now I’m using 102mm and getting used to them. The other two main sizes are 110 and 89. 89 is very short, but they work well for UNICON X World Champion Kazuhiro Shimoyoza.
Long cranks offer more leverage and control. Short cranks smooth out the oscillations of pedaling, and improve high speed riding, spins, and one-foot skills. But the lack of leverage can make learning the skills a little harder.
SEAT:
Use what’s comfortable! If you don’t like your seat, you won’t ride the uni as much. I still prefer the Miyata seat with air, though I’m waiting for my first Velo to compare.
Seats with handles are cumbersome for Freestyle. Many expert riders have cut off the handle from their Miyata seats. This has the effect, on the newer Chinese-made ones, of fixing the problems with those things breaking. Some people also just take the front bumpers off, but I don’t recommend that as it will lead to a chewed-up front on your seat.
CONCLUSION:
The best way to approximate all of this is to order a Wyganowski, if your budget allows. Otherwise, you can piece something together, but add up all the costs first, to make sure you don’t come out about the same in the end…