Im 16 and wanting to join a gym, how would this stunt my growth or what exercises would stunt my growth?

Likely won't at all: To be honest, unless you are lifting very heavy weights your growth plates should be fine. Resistance training is fine but try to avoid maximal weight(as in single repetition weight) training.

At 16 most of the --: growth should have been completed enough that it would not be stunted. You can do all and any exercises you want.