Linux Gaming

DS5 is probably the best you can choose. The build quality is good and they work fine with Linux via Bluetooth. Also it is not some exotic choice and is widely supported.

The Xbox controllers are also working fine, but they are lacking the gyro and touchpad. Also the build quality wasn't great when I used one the last time (A button not registering every press and wonky d-pad). They are a bit cheaper, but also much worse imo.

8bitdo Ultimate 2.4 Ghz, it connects with a dongle, but if you update the firmware you can use Bluetooth as well, even though they don't advertise it. You can also go with the Ultimate C 2.4 Ghz which doesn't have the back buttons or mappable buttons (I don't even know if 8bitdo's Ultimate software works on Linux) to save some money.

Xbox Series X controller with the Windows Adapter: https://www.xbox.com/en-US/accessories/adapters/wireless-adapter-windows it's the standard for computer controllers. Used by over 50% of the market. With the Linux Xone driver, it has some pretty good Linux compatibility but you just have to ensure you set it up correctly. You can also use the Xbox Series X controller to use Bluetooth but it comes with the drawbacks of higher latency and less range. If you plan on doing that use the xpadneo driver instead.

The Playstation 5 controllers are the next popular and the next ones I would recommend. They have less driver support on Linux for some of the more fancy features such as the touchpad and sixaxis do not work over wireless.

@TxTechnician Xbox One S controllers work pretty well on Bluetooth. I can connect 4 controllers at the same time but more than 2 is not really stable. And if you don't mind some tweaking, they work better with https://atar-axis.github.io/xpadneo/.
I also used Logitech F310 without any problem. Oh, and steam controller works well too.

8BitDo SN30 Pro works great. I'm using the Xbox edition that's meant to only work on Android with Game Pass thanks to xpadneo drivers