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.
I haven’t used EmuDeck since they’ve apparently revamped the installation process, but I think RetroDeck is (or at least was) a much cleaner installation since it’s just a flatpak. I’ve got it installed on my deck and it works fine. Not really using it atm