@emulatre71 @windg thanks for chiming in, yeah I actually do already have the F310 and am a fan for the most part (I did find the fact that you couldn't seem to program the Mode button on Retropie a bit disappointing, but that was before I knew that the Logitech logo was itself another button).
That F710 is a bit more expensive but I may look into that if I want a PS2-style wireless controller. Bluetooth would be ideal, but if indeed the Pi has issues with bluetooth devices I may just have to either get a USB hub (although I've heard that there can be issues powering them/that one might need to get one w/ an external power source, which could be kinda a hassle) and plug the 4th controller's dongle into that, or simply have to unplug the keyboard if we're playing a 4-player+ game.