Remote?

I just use an xbox controller.

8bitdo with their wireless adapter

Wireless mouse and Xbox controllers do most everything I need.

If you mean for gaming, the Dual Sense is awesome. Although gyro control has been broken for months. If you mean for media, the Pepper Jobs W10 Gyro is awesome.

XBox elite controller.

I actually use the paddles on the deck, so it's nice to have them on desktop and when docked. It's not cheap, so it tooke a long time to pull the trigger on, but glad I did.

Steam controller or PlayStation, depending on the game.

To answer your question: I use an Xbox Series X gamepad. However I cannot recommend this cheaply built piece of junk.

I also tried to use the DualShock 4, but with that I had the problem that it interfered with my WIFI connection. I'm not sure if this is a general problem, or only happens with my WIFI base station though. Also, the DualShock controller has a severe drawback, and that is its short battery runtime, compared with the issue that you cannot easily switch batteries...

So, my recommendation: An Xbox One gamepad. While I don't own one, I am using them regularly at work, and they basically have all the advantages of the Xbox Series X gamepads, and have a way better build quality.

I would also recommend Xbox 360 gamepads, but they need a dedicated base station, which is very expensive.

My Xbox Series Controller, my Dualshock 4, my Dualsense, my Steam Controller, my Switch Pro Controller, My 8bitdo Ultimate Xbox controller, basically whatever is within reach, they're all fine but I like the 8bitdo best.

Just use whatever you already have. If you don't have anything I'd say go for the 8bitdo or the Xbox Series controller. They're both excellent. The Switch pro has the buttons backwards, the PlayStation controllers don't have the best build quality (I've gone through multiple of each even though I treat controllers kindly), and the Steam Controller is a little weird and not sold new anymore. So Xbox Series if you want to save money, 8bitdo Ultimate if you just want the best.

You could consider using a USB C extension cable. That way you can use the Deck’s built-in controls. I either do that or use my Steam Controller.

I don’t think most controllers are worth their price. I got a Bluetooth Xbox controller once and it was expensive, lacked features, and broke way sooner than it should have.

If you don’t need a wireless controller you can get a Logitech F310 for pretty cheap and I find those nice to use, but they don’t have trackpads.