I personally wouldn't get a bluetooth mouse for gaming. Besides with bluetooth you always get some problems... either with batteries running out or that it "cannot be found" by the computer.
Save yourself some unneeded pain and get a corded one!
I personally use a Microsoft (yes, i know! I always hide it when someone comes around) Comfort Mouse 4500. It does not need a mousepad(something I love about it) and it is wired. And nowadays you can get one from amazon for 8 dollars.
Only slight minus on this one is that the scroller has no or very little friction to it...