8Bitdo Ultimate Bluetooth. I use it with the included dongle and it works just fine on my distro (Nobara). Kubuntu should also be fine I guess, just make sure you're on a recent kernel (6.3+)

The main reason why I'd recommend this over others is that it has built-in macros - which is really handy for some games where you may need to press a complicated button sequence (like in fighting games), and of course, it also has the classic "turbo" feature which is handy for platformers.

The other reason is that the controller also works great with the Nintendo Switch as well as Android, so if you ever decide to game on these platforms you can reuse the same controller.

Edit: I just remembered that when I first got mine, I needed to update the firmware to get it to work correctly. You'll need to update the firmware on both the receiver (v1.03) and the controller (v1.05). You'll need to do this one at a time (update the receiver first, disconnect it, then connect the controller directly via USB and update it). Unfortunately the firmware updater tool works only in Windows or macOS, so that's one drawback I guess. But maybe in the future it could get updated via LVFS/fwupd.

Steam Controller 😭

Can’t comment on Linux compatibility. But on my windows PC I use a Gulikit King Kong 2 Pro. Really like it so far, no major issues, pretty good battery life.

DK Bongo Drums

Anything 8bitdo.

I haven't had any issues with my DS4s (PS4 controllers), and I've heard good things about DS5s. I've also used XBox 360 controllers with a dongle.

You could also look for Stadia controllers in case you can find a good deal. Stadia was discontinued, but they can be updated to work like regular controllers, at least through the end of the year. I don't have any direct experience with them though.

If you have bluetooth on your PC you can use any Xbox controller (from Xbox One up). They are the perfect standard. Grab some rechargeable double As and the controller will last literally forever and is compatible with everything. Or a battery pack even from third party brands. I know many people complain about it using double As but its actually a great thing, double As last 20x longer than any battery and you can use rechargeable ones and don't worry about your controller dying as it ages.

The new 8bitdo one with hall effect joysticks is very nice. Has both Bluetooth and a wireless dongle and there's a hardware switch on the back so you can switch between them on the fly (meaning you can connect two devices and easily switch between)

I've used a few controllers. Generally, controllers with direct input have worked the best. My favorite controller to use is the Dual Sense controller(PS5). The Switch controller also works right out of the box. Xbox controllers seem to be hit and miss. If you do want an Xbox style controller, consider the 8bit-do ultimate controller, as it has a dinput mode. Avoid the Bluetooth variant, as the 2.4ghz mode is xinput only.

I use a DualSense, an 8BitDo Pro2, and a Switch Pro controller.

My favourite by far is the DualSense: motion control works (unlike the 8BitDo), and the touchpad is really useful to control the mouse cursor in menus. The buttons are also shorter and real more reactive. It's on the bigger size, which may or may not be a good thing for you. I have smaller hands, so for me it's not as comfortable as the 8BitDo, but it's definitely bearable, and I still use it over my 8BitDo Pro2.

The Switch Pro controller is a pain in some games (last time I tried, it was so bugged it was unusable with Dead Cells), and I don't see any real advantage it would have over an 8BitDo Pro2. Maybe the motion control? I don't know if it works or not, I have never tested it.

I’ve had really good experiences with PS5 DualSense controllers. They connect via Bluetooth or USB-C and have official support for the Linux kernel. The touchpad also works as a mouse out of the box which is really convenient.

The Xbox one is good and it's the standard layout on PC, so this is probably your pick.

I love my Steam Controller since is very customizable and a pretty unique hardware, but it may require config steps.

8bitdo stuff is usually good but pay attention on layout buttons.

Never tested a PS controller on PC but Steam should allow to play some game with the PS buttons on screen.

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.

Personally waiting for the leaked Xbox controller to come out.

I am using the Xbox One controller. I had to pair it with Windows once to fix a connection problem, but now it's problem-free. I'm pretty sure that the problem and solution was described on Arch Wiki but I can't find it now. Basically it was stuck on disconnecting and connecting again until Windows didn't update its firmware

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.

@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.

I like the dualsense5 controllers for the PS5. The trackpad is a handy feature to have.

You should be able to use pretty much any Bluetooth controller just try to avoid the Bluetooth low Energie LE controller my stadia controller that i resenty bought doesn't work on many distos Nobara no problem if you use arch forget it

Both the PS5 and Xbox Series X controllers are very good. I've had some incompatibilities on my computers with older bluetooth hardware though. Speaking practically, I'd recommend the Xbox one as it's slightly cheaper, takes regular replaceable batteries. Subjectively, I prefer the PS5 controller (I like the feel, and the trackpad is really handy), but I've already had to replace the lithium ion battery in mine. (Had to do the same with my older PS4 controller too)