Myself being a club president in the 10th month of his 12 month term is the worng person to ask, but here goes :) most people start a car club to get folks together to share a common passion of these old cars, or any cars for that matter. In the beginning a car club is a very innocent thing, but hten as it grows comes club goverment, by laws, regulations, dues and lord knows what else, it seems to never end, officers to be elected, by-laws to ammend, and anytime you get a large enough group assembled you'll have folks that very passionately disagree on matters, now most people can't disagree on club matter and leave those diasgreements on the board table, but others will let it enter into your personal life, that is exactly what I'm dealing right now with within my club.
So take advice from a fool who has been a vice president, and now is president and soon to be board member of a car club. Join one near you, sit in the back of the room and leave running the club to ones who aspires to do such things, lord knows I wish I had not been talked into being a officer, if you do this, your car club experience will remain very innocent, but if you lift the lid off the jar of club goverment or club management, be fully aware it always doesn't go smooth as planned.
As far as your questions
we have yearly dues of $25
The president and many dedicated members will help in the planning of events, we have array of events each year, tech sessions, social outings, car shows both helping put one on, to canvoying with member to area car shows, to club rides in the mountains.
As the group grows so do club responsibilities, like electing officers, writing by laws, newletters, websites etc. Our car club with about 80 or so member has became very involved to keep running smoothly, it take several folks to do certian jobs, and it always seems you are constantly looking for your next victim :) to fill the shoes for a vacant position.
As club president I'm no longer niave about the internal workings it takes to make a car club run, I wish sometimes I was, but then next time I wouldn't be smart enough to say no :) Personally I can't wait until my presidency is over, I don't have to secure meeting places, conduct meetings, write group member emails, hold board meeting, etc., etc, etc.. I can then just get back to being a regular member who maybe helps put on a tech session or group ride, and doesn't have to worry anymore about help running a car club.
I'd be interested to hear other club presidents (past and present) chime in.