Thanks for the detailed response.If you want new, then Logitech G F310 is an option.
If you want to consider used:
• If your PC has Bluetooth 2.1+ and if you can stretch your budget, I'll plug this thread by @joy.das.jd (installing 'DS4Windows' should make a DualShock 4 function like an Xbox 360 controller).
• If you can stretch even further, this one would probably be better.
• If you don't mind some more visible wear and tear, you could also check in with @andrew327 about a possible 360 controller and receiver combo from his thread.
I bought what seemed like the nicest of the three, and there's zero drift thankfully, but I can't vouch for the others obviously.360 controllers are very old so stick drift will be there.
No such thing requiredThe F310 should be a solid choice, but it might lack vibration/force feedback/rumble, if that could be a deal breaker.
If i was in same city as you I would have taken you up on that offerI have a logitech f310 which I don't need. It's old though. Let me know if you need it. I won't charge anything but won't mind a pizza.