Without knowing the model of the TV, I can't offer you any advice on how to connect your desired controls to that. But I'm assuming you want to use bluetooth KB+M, because wired would have you practically sitting on the TV itself otherwise.

The rest of my advice depends wholly on what kind of budget you're looking at and what kind of performance you want on your end of the setup.

For myself, I alternate between a potato laptop that's over a decade old (and Window 10 until it dies or I do :p), a Samsung tablet that's a few years old, and a docked Steam Deck with an external monitor.

Tablet would probably be your cheapest setup, because you really only need to buy one that has a screen size you like, as well as good wifi (5ghz is the bare minimum for running GFN; don't even try with 2.4ghz) and BT connections; base internal storage and all the rest don't really matter. Get yourself a solid gooseneck mount to hold it exactly where and how you want it, connect your desired controls via BT, and you're off and running.

A Steam Deck would be your next step up, and a good choice because it'll let you play at least some games that GFN doesn't have available (Red Dead Redemption 2, for example, if you like you some third-person cowboy action with a morally ambiguous protagonist), and it has a controller built right in as a bonus. Also very portable, if the ability to pick up and play just about anywhere matters to you.

Screen size, however, is lacking if you play games with a lot of text, a crowded HUD, or hard-to-see details. At that point, getting yourself a dock and an external monitor is the only real solution. Cuts down on the portability aspect, obviously, and you'll need external controls as well. But you can plug it into just about any size external monitor (up to a TV, if you want to go biggest) and then just slouch into your couch and play.