My main stopper for watching avatar, which I gave 3 episodes like 2 years ago, is how childish it is. The main char's like 10 years old and watching him fumble around and be awkward is... I'm sure it's a good show but sighs, hard to get over that.
The game though, I see you're a waifu academy fan. I love that game, how is this game in comparison?
So, in defense of Avatar, yes, Aang does start out childish. There's reasons for that, one of which is that he's 10. But! That's the whole point of the show, in that a 10 year old has to learn how to accept the responsibility of becoming the Avatar. The first half of the first season is showing what Aang is, the rest of the series shows what Aang becomes. All of the characters have really good arcs, including the villains. Also, it has some of the best world building I've ever seen, and by the end it gets fucking epic.
If you have the time I would really suggest powering through the first 10 episodes. If you don't like it by then, then so be it. But, if you like epic fantasy with great characters and some genuinely funny humor, give it another chance.
Also, on the other question about having to watch the show to play the game: Naw. It would help to give some background on the characters, but, you don't really need it.