Wheels are by no means the only way for a bot to actually move across an arena floor. Walkers and treaded bots have an added coolness factor, and walkers also have a special weight advantage. But each is hard to pull off. If you are inclined to go out and try either, go right ahead, as these type of drive systems can make fans based off of sheer looks at times. Otherwise, though, why reinvent the wheel? The wheel is a simple form of translation for a bot. The bigger the wheel, the further the wheel travels in one rotation. This is because the distance a wheel travels in one turn is the length around the wheel, or the circumference, which is equal to pi (3.14) times the diameter of the wheel. As diameter increases, so does distance per rotation.
But like many things in fighting robotics, there is a drawback. The bigger the wheel, the less the pushing force a bot can have. This is because pushing force is partly determined by torque (see motor sections), and torque's effect lessens over distance. Since the wheel turns by pushing against the ground, force becomes (torque at motor shaft)/(distance to ground, or radius) (from t=fd, f=t/d). The force also takes into account the number of motors spinning at the same time (more in the same direction increases total force on the bot) as well as traction.
Traction is, roughly, how sticky a wheel is. If you spin an ice wheel on ice, would if propel the bot very forcefully? No, it would skid crazily (and melt, probably). The more traction you have, or the more friction you have between your wheels and the surface they rest on, the more force they can actually have from torque. This goes to physics: there's a concept called the coefficient of friction. Friction is equal to the force the ground exerts on you (or that you exert on the ground) times the coefficient of friction. This coefficient is a constant that is different for all surface combinations in question. Rubber on pavement is close to 1.0, the maximum value of the coefficient of friction, and ice on ice is close to 0.0, the minimum (about frictionless). With 1.0, one can push something their own weight. There are other things that affect this, but it's a good way to estimate.
Anyway, if a coefficient isn't out there, just feel the wheel you are considering. Try to roll it. Does it try to resist spinning in place? The more the better.
What about width? How does this affect wheels? The wider a wheel is, the more it wants to resist turning, and the thinner it is, the harder it is to drive straight. Thin wheels are also lighter, but wider wheels are less likely to break. Did I mention that trade-offs are common when building bots?
Anything else to consider? How about attachment? How can you attach your wheel to the rotating part or motor shaft in the bot? Make sure the rotating part has almost total control of the wheel, virtually no play, and maintains control when suffering jolts as it will in battle or during a sudden start or stop. Otherwise, you may regret it later.
Finally, consider the distance between the centers of your wheels. The closer together your wheels are in non-car steering bots, the quicker it can spin in place. This gives is a quick reaction time (and can make it dangerous as a "thwack" bot), but also makes it harder to control, as well as more likely to topple over if hit from the side. Tradeoffs! Gotta love 'em. To calculate the spin time of your bot, figure out the speed of your bot. Then figure out the distance between your wheels, multiply by pi and divide the result from the speed of your bot (make sure the distance unit in your speed and the distance unit in your distance line up (meters/sec and meters, for example)). This is because the bot turns in a circle with edges in the centers of the two wheels (in a two-wheeled bot) and a center in the bot center. You are taking the circumference of the path each wheel takes, then dividing it from the speed to figure out the spin rate (rev/time, where time is whatever unit you used in your calculation). I simplified the equation - spin rate in RPM is: ((wheel diameter/wheel distance) output RPM).
Congratulations! You have mastered the science of wheels. (If you had only managed it before the cavemen, then you'd have it made.)
