Optical mouse: Not for FPS games, use it on a consistently coloured, stable surface. I find darker sufraces are better but anything is better than a mousemat. Do not use an optical mouse with a mousemat - especially one with logos and images all over it (this is what causes the jumpy behaviour). I've had the same optical one for about 6 or 7 years and it hasn't failed me yet.

Ball mouse: Good for FPS games because you get better control from the ball (ability to turn quickly etc). Needs regular cleaning out and a mousemat is advisable.

Wireless ball/optical: Same thoughts as Lemur, I don't see much benefit unless you want to operate the PC from 10 foot away. Also there's the batteries to be bothered about... etc.