Congrats! I think the number one thing I didn't know is that when you have a question, it's totally okay to call your AEA rep! They are there to help. A lot of AEA questions that come up are situation-dependent, so you can't necessarily get a clear answer by asking someone else. Sometimes a particular theatre will get a special concession from Equity about a particular rule, so something that's okay at one theatre or on one contract might not be okay at another (or vice versa). I've never had a rep mind me calling and asking, and it's usually the quickest way to get a question answered. If you don't know who your rep is, ask your production manager (or whoever handles AEA contracts at your theatre).
I also think it's really helpful to print out a hard copy of the rulebook for whatever contract you're working on and put post-it flags on any rules that you might want to reference quickly. For me it's usually things like the rules regarding rehearsal and performance hours, how many hours of fittings are allowed, etc. So much easier to reference them quickly. (Though the search function on a pdf is helpful too!)