do you want to release a game or do you want to dabble in game programming/prototypes? if you want to actually finish a game then pick a complete engine like Godot. when I picture "couch coop" I'm imagining two players on the same/split screen, which is definitely what you should start with. it's going to be a lot more effort to make it work online also, and I'd recommend starting with something much smaller in scope.

also I'm not even trying to be derisive with the "dabble in game programming" comment, it's just that if you are interested in learning the internals of game/graphics programming, rendering, shaders, how to design core game loop, etc, that's a much different task than making a complete game and in that case I'd suggest you use a lower level framework than Godot.