All the above advice is good, especially scheduling. Adding a couple of things:
If it's an equity club, and you have to "buy in" with a significant amount of money, sort out how you get that equity back if you want out. That sounds simple, but if the club has a fixed set of members, say 35, and they change that number in the future to 25, then if you quit you might not be able to get that equity share back for a long time. That goes along with the suggestion to read the bi-laws, but understand they can be changed. Really you're going to be a minority owner of a corporation, so anything you put into it could be lost.
As an add-on to the above, find out what happens if the club decides to shut down. In some clubs, non-aircraft, there are multiple classes of members, and the initial tier may have more rights to what happens with what's left. No idea if this is possible in an aircraft club.
Finally, before joining I'd check to make sure the club is currently registered as a corporation in your state, to limit your liability. Some clubs start out that way, but someone doesn't pay the state corporation fees for a couple of years, and the corporation is dissolved. In some states it's possible for that to happen without the members noticing. I'm not an attorney, and liability to general members may be nothing, just something I keep in the back of my head.
Go to a meeting or two and see what they are like. Most groups are normal, but some have a weird tilt on things...usually easy to spot. Be careful with volunteering, clubs of any sort can be an incredible time sink. I'm not saying that's bad at all, just to go in eyes open.
Most of my ramblings are based on being on the board of a couple of non-aviation clubs in the past, and having dealt with the fun that goes along with that. Some of it might not apply to aviation.