luigi_m. You've just described my club.
Well, almost. The airplane variety is a little different. With a fleet of C152, C172, PA28-161, PA28-181, DA-40, DR200-120, DR200-160, DR200-135CDI and a R2160 we have just about everything you might conceivably need as a PPL. Through club members we have access to an Arrow (for complex ratings) and a Seminole (I think) for multi-engine. The R2160 is of course used for aerobatics, including competition. We have a formation team that regularly flies 9-ship formations. The only thing missing, really, is some sort of tailwheel aircraft. Maybe a vintage aircraft or a CAP10C or something. And it would be nice to have one or two plastic fantastic, Rotax 912 powered two-seaters for very cheap touring.
Oh, and there are various club events throughout the year. Flyouts (Flying Legends @ Duxford), club weekends/weeks and a rally competition held throughout the year. Some club flights have been as far as the North Cape, to Lands End, Eastern Europe and to Morocco, and that's just the ones I know about. More locally, we have an annual Goodwill day where we take young patients from some nearby hospitals flying (last year we had close to 100 patients spread out over some 60 flights), we have the annual Open Day where people can get cheap trial lessons, flight sim events and the occasional party.
What is really, really important is that the people who "formally" run the place (the board or CFI) give others the freedom (and encouragement) to organise things. Don't try, as a CFI or other hotshot, to be involved in everything. Even people who barely have their PPL might be wizards at organizing things like charity flights, open days, flyouts etc. If you have a dozen or so enthousiast volunteers and you manage to keep them motivated, you've got a proper club.