For general use/productivity, I recommend the Logitech MX Anywhere. Been using it for over a year, no complaints. Upgraded from a cheap-o, no name, unbranded $10 2.4Ghz piece of junk and the two are worlds apart. I game with a gamepad because scrub, so I can't attest to the Logitech one way or the other in that regard. It doesn`t have a wired mode to my knowledge, but the battery is rechargeable so if the reason for your insistence on a wired mode is battery anxiety, you're covered on that front.
Also, do people game with wireless mice? I was always told latency was a concern and to stick to wired mice for that reason.