First of all if you join a real boxing club they will expect you to spar and fight competitively if you want to just get in better shape join a cardio boxing class. Now if you do want to join a real gym $150 is pretty steep look for a different gym or try kickboxing, also height wont matter because there are weight divisions.
That seems very expensive from the countless gyms I have trained at it is more than almost all of them try another boxing gym check hear-http://www.boxinggyms.com/
That gym isn't going to teach you properly. It's not there because of ex fighters wanting to pass knowledge on but for profit. My gym costs me £2 week.
I wanna join a boxing group to get physically fitter (im already pretty fit) but mostly to hae better boxing skills. Is it worth it to join at $150 a month? Idk if i can afford more than a month every few months because I'm only 16 and jobless. I'm also 5'10 if that changes anything