I use a wireless Logitech mouse for gaming, and I havent had any issues with lag. Now as kyfire said, it does suck when the batteries die in the middle of a match, so you're going to want to keep an eye on the low battery light. problem is your budget. when I got this mouse years ago (probably 8 or 9) it was over $100, and I doubt you're going to find a good one in your budget. I'd recommend mine, but I've had it for so long that all the markings have worn off, so I have no idea what the model number is.
Ic. USD100 just for wireless mouse sound very crazy to me ) few days ago, the keyboard is ok i didnt sense any lag when typing or gaming but the mouse like moving too fast or too much or something (not sure if it cause by 2000dpi or not) no matter in desktop or in game, or may be i should use lower dpi mouse ??
By the way how long a battery normally last ?? Few days ?? Few months ?? I do take out the keyboard battery and turn off the mouse as well when not using.
Many thanks for all your time