Consoles have used different wireless tech/protocols but mostly use bluetooth now. Bluetooth devices should be able to work on pc but may require extra hassle like non standard protocol and no official drivers if they weren't intended to be used that way. For the ones that do work the main takeaway is no additional dongle if your system already has bluetooth, but there may be addititonal input latency.

2.4ghz is kinda silly naming because bluetooth and wifi are both 2.4ghz, though wifi also has 5ghz, but it usually refers to presumably proprietary protocol over 2.4ghz and uses a usb dongle. It will generally be faster/lower latency but that isn't even guaranteed as the 2.4ghz mentioned never refers to any standard.

The latency difference will only be noticible to cats or birds or something unless the controller tries to pass the headset audio to the pc. Bluetooth audio has a noticable delay compared to most '2.4ghz' options, particularly noticable in rhythm games, games with inputs timed to audio cues, voice chats where everyone else has low latency audio and fast internet, and probably other stuff I'm not personally into.

Deciding your controller comes down to a lot of things. If the means exist in your area, try as many as you can to determine your most comfortable size, shape and layout. Other than that you absolutely must do yourself a favour and get a controller with hall effect sticks. The console companies all love stick drift. Don't be fooled by Sony's replacable stick controller either, the sticks are always out of stock and if you can solder you can get a regular controller and swap to hall effect yourself, both sticks, when drift starts for like $5 CAD vs $25 for 1 that will eventually die in the same way.

But probably just don't give m$ sony or nint your money since they all get drift and I have replaced the battery and charge circuit on 8 separate ps4 controllers and drifting sticks on so so many of every big3 console controller. 8bitdo has a few stick and trigger hall effect controllers which I can mostly recommend, I have the hall stick only version of the ultimate controller and several of their older regular stick controllers. They are noted for their very close replica feel of snes dpad and face buttons but the configuration and firmware update software was windows only last I checked. I also quite like retro fighters controllers but all of their hall effect options are on closed preorder pending fulfillment. There are other highly regarded non big3 brands that I haven't tried that seem to have pretty solid feature set and build quality too.

The used market is also an option. Arrange for testing though, and pass or haggle on drift, charging problems, filth, etc. Ifixit teardown guides for swapping parts or just cleaning the shells and button caps in soapy water with a soft rag. Watch out for devices originally sold with 'soft touch'/'smooth grip'/etc finish as all of them have degraded and become sticky even unopened in box by now.