The Front Wheel
Front wheels for a fixed gear bike are often the same as a standard bike wheel. A true front “fixie” wheel will bolt on (with nuts). However, a wheel with a quick release skewer will work fine.
The Rear Wheel
The rear hub is where the difference is. At the very least, the rear hub will have two sets of threads on one side of the hub. The larger of the two threads receives the fixed gear cog. The smaller set uses consists of a left hand thread that a special lock ring goes onto. This lock ring stops the cog from coming undone under heavy “back pedal” pressure. When slowing down on a fixed gear bike, backward pressure is applied to the pedals.
New or Old (used)?
When deciding on a fixed gear wheelset the lowest cost option is to go the used route. If you are converting an existing bike, the front wheel can often be used. The easy “rear wheel solution” is to buy a new rear wheel with the special hub as part of the package. Of course, for a matched set, a complete fixed gear wheelset purchase is the way to go.
Most front wheels fit a fork that is 100 mm between the fork tips. Rear wheel spacing, however, can be all over the place. The distance between the dropouts of a bike can be 120 mm (standard track bike or fixie dimension), 125 mm, 127 mm, 130 mm, or 135 mm (or a variance of all the previous dimensions). Be sure you have the rear hub spacing to match your frame. If the frame is constructed of steel, a quality bike shop can often tweak the dropout distance for hub spacing.
The rear cog size is important and usually the last consideration. If your fixed gear frame has road or track dropouts, virtually any size cog can be used as you will have ample dropout adjustment to achieve proper chain tension. If you are converting a bike that previously used derailleurs and has vertical dropouts, finding the proper cog size will depend on your front chainring size and chain fit. Vertical dropouts work fine on multi-speed bikes because the derailleur jockey wheel cage takes up the chain tension. However, with a fixie, no such chain tensioning is available. Some fixed gear hubs have elliptical mounting flanges to allow for chain adjustment.