I have an xbox elite pro series 2 that my wife bought me last christmas. I love it. It has a good weight and is a joy in your hands. The triggers have 3 resistance levels. D-pad and thumbsticks are magnetic and easily swappable. Four back paddles can be removed easily if they're not wanted or needed. It connected to Pop_OS via bluetooth with no issues. I have not tried using the xbox accessories app on Linux because I was able to calibrate it with Steam just fine. Thry're not cheap but it was worth it.

Edit to add: someone mentiomed drift and I did have a slight issue but was able to adjust for it through Steam. There is also a common complaint that the controllers snap back to center with enough force to actually hit the opposite direction; most commonly noticed in metroidvanias or other 2d platformers where it can make you turn around unintentionally. I was also able to adjust for this with Steam calibration.

I use my PS2 and PS1 controllers with a converter to PS3 (USB). Debian by default converts the controller to a XBOX360 one (more precisely, the default Duelshock 3 driver does), making it generally supported.

Dualsense with a back pedal mod is king tbh. Very easy to set up with no soldering needed.

I think the only thing that could beat it is something like 8bitdo which integrates the extra buttons into steam input, but they don't have a controller that's as good, and from what I've heard their upcoming pro 3 controller that's got the playstation layout isn't that good, especially dpad-wise.

I use a DS4 and used a DS3 for years before that.

Using none Xbox controllers on PC used to be a pain, I remember the hoops I had to jump through to get my DS3 pad working with Windows 7. Now it's easier than ever.

I actually didn't like the DS4 controller for the longest time because of the thumb-sticks but found some replacements a while back that has the more comfy (to me) domed design of the earlier PS controllers.

Amazon Link, couldn't find them sold anywhere else in the UK sadly...

Neigsendoig and I use a PS4 Dualshock, though if we were to get a different controller, we don't know how well that'd work for us.