360 wired, no doubt. It’s the only one that will really guarantee compatibility. Wireless has a common problem that Microsoft doesn’t seem to want to fix (right trigger non-functioning) and that developers don’t seem to want to work around sometimes.
Just get a x360 controller, wired. You plug it in and it works - amazing. I had an admittedly entry level Logitech pad that was annoying, always needed stuffing around with setup, mapping etc to get working.
If you get excited, upgrade to one of the more exotic ones later.
I got the Razer Onza recently. It’s a 360/pc USB pad, and their d-pad has a different design…similar to the playstation’s plus pad in that the directions are separate buttons. I haven’t tried it yet, so someone else will have to give their opinion.
The real 360 controller? The D-pad is “mushy”, in that you think you pushed right, but it registers up-right or down-right, or sometimes even down or up. It is impossible to many people to play street fighter and pull off a fireball or an uppercut input consistently. (SF4 works around the problem by changing the input.)