I'm not much of a "joiner". Can I form my own club and be the only member?
Even if you're a loner, the advantage of being in a club is that you can get ideas from other folks. Also, it's a good place to get rid of beer if you have too much!
As for club size, I think that olllllo pretty much nailed it. The leadership has to plan for growth or limit growth. Planning for growth has its own problems. Limiting growth can be problematic in that you turn away potentially great people and acquire a reputation for snobbishness. Also, what do you do with current members who temporarily turn into "dead weight" (i.e., stop brewing, don't come to meetings)?
From HB clubs in my region, I've see the following structures:
1) Small and informal - 5-10 people, usually friends, who informally meet, usually in someone's house. No real officers, no dues, no formal club functions.
2) Semi-Organized - 10-30 people, maybe not so tightly linked, who meet informally at a restaurant or bar. Might have officers, by-laws and membership dues. Might sponsor club events.
3) Small Organized - 30-100 people, usually with formal officers, by-laws, dues and so forth. Might be big enough to run an annual HB competition and hold similar club-sponsored events. At this level, there are some logistical strains and the possibility that new members are either not welcome, or feel ignored.
4) Big Organized - 100+ people, as above, but more organized and possibly more formal. At this level, budgets and logistical issues get big enough that the club starts straining unless it's got a very talented cadre of leaders and support people who want to make the club work. At this level, even finding a suitable venue for club meetings can be a hassle, and visitors and new members can feel excluded.