The wireless Xbox360 controller works in Linux, you just have to get the Xbox360 Wireless Receiver adapter (sold separately or bundle with the controller, depending on which version you pick). For USB recharging you also need the Play&Charge kit, which is sold separately, normally the controller just runs on AA batteries and can't be charged with a regular cable. Also note that Play&Charge cable is for recharging only, it doesn't transmit input data to the PC, the Wireless Receiver is always required for the wireless controller.
XboxOne controller doesn't yet support wireless communication, but that might come in the future. It can be used with a regular USB cable, but I haven't tested that myself.
PS4 controller might also be worth a look, but I don't have any personal experience with that one either.
The most popular X-input controller I can find is this razer sabertooth.
It is the most used and praised 3rd party PC controller I can find but is expensive (60 usd+).
However ANY xbox 360 or xbox one 3rd party controller will work fine but bare in mind that you need the official wifi adapter from microsoft for most of these as xbox's don't have bluetooth.
Also ANY Playstation 3rd party pad will work with some tinkering but the results can vary.
It would be best to get one with its own receiver bundled in, as compatibility is an issue, and if you want steam game compatibility AVOID direct input, and buy X-input, it can work but is outdated.
The big issue with the 3rd party PC game pads is they are often very chatty with shit buttons and latency issues, I very much recommend not buying any cheap PC game pads EVER as they suck, like this one - LogitechF710
EDIT: Heres some others I found HERE and HERE, they look good but are PS3 branded so no X-input, and you will find a few HERE too.
No X-input is not the end of the world though, install xboxdrv to make it act like xinput
sudo apt-get install xboxdrv
As a side note a X1 pad will now work with steam and they are hands down the best option.
The wireless Xbox360 controller works in Linux, you just have to get the
Xbox360 Wireless Receiveradapter (sold separately or bundle with the controller, depending on which version you pick). For USB recharging you also need the Play&Charge kit, which is sold separately, normally the controller just runs on AA batteries and can't be charged with a regular cable. Also note that Play&Charge cable is for recharging only, it doesn't transmit input data to the PC, the Wireless Receiver is always required for the wireless controller.XboxOne controller doesn't yet support wireless communication, but that might come in the future. It can be used with a regular USB cable, but I haven't tested that myself.
PS4 controller might also be worth a look, but I don't have any personal experience with that one either.
The most popular X-input controller I can find is this razer sabertooth.
It is the most used and praised 3rd party PC controller I can find but is expensive (60 usd+).
However ANY xbox 360 or xbox one 3rd party controller will work fine but bare in mind that you need the official wifi adapter from microsoft for most of these as xbox's don't have bluetooth.
Also ANY Playstation 3rd party pad will work with some tinkering but the results can vary.
It would be best to get one with its own receiver bundled in, as compatibility is an issue, and if you want steam game compatibility AVOID direct input, and buy X-input, it can work but is outdated.
The big issue with the 3rd party PC game pads is they are often very chatty with shit buttons and latency issues, I very much recommend not buying any cheap PC game pads EVER as they suck, like this one - LogitechF710
EDIT: Heres some others I found HERE and HERE, they look good but are PS3 branded so no X-input, and you will find a few HERE too.
No X-input is not the end of the world though, install
xboxdrvto make it act like xinputAs a side note a X1 pad will now work with steam and they are hands down the best option.