Well, if you join the AMA in a non-leadership capacity, they will give you something for "free" when you pay them. From there, you can continue to write them checks, and they will send you e-mails and let you talk to other people who also paid them on their forums.
If you join AMSA, you can pay them for something "free" as well. Payment into this club grants you the privilege of being elected to an extensive board, where you can work for free to produce fund raisers for AMSA, getting the group more money.
Keep in mind you can still attend most events from either organization whether you pay them or not. You can even get their e-mails. The only difference is, you're not a paying member.
What I would recommend instead of just joining clubs so you can say you joined them (by paying), is to get involved in activities you actually enjoy, and in which you can perhaps rise to some meaningful leadership position (which is possible in both of the above groups). Much like applying to med school, fluff hollow extracurriculars are quickly uncovered on the residency interview.