A good gaming mouse comes either way now, so the choice between wireless and wired is mostly about how you like to play.
Why go wireless
No cable drag, nothing snagging on the edge of the desk, and a cleaner setup. If you play at low sensitivity with big arm swipes, losing the cable is something you feel right away.
Why go wired
No charging, ever. If you're the type to forget to plug things in, wired removes a whole category of problems.
2.4 GHz vs Bluetooth
For gaming, use the 2.4 GHz receiver. Bluetooth is convenient for laptops and everyday use, but it isn't designed for the fast, consistent reporting games want.
Wireless tips
Keep the receiver close to the mouse — an extension cable that puts it on your desk instead of behind your PC helps. And charge on a routine rather than waiting for the low-battery warning.
Whichever you choose, fit comes first: see choosing a mouse for your grip, then browse mice. Cables and skates are in accessories.