Have you looked at Positive Internet? Full ssh access, mysql, mod_perl, the works. You can add your own modules, but normally you're better off asking the very helpful tech support guys to add the module to the server so everyone can use it.

From experience on a cgi/database heavy site (http://www.moonfruit.com), mod_perl is *essential* if you are anticipating scaling to larger numbers or users. "use strict" and you'll have no problems with mod_perl.

MySQL has limitations, but is cheap. No transactions (OK - no "normal" transactions...), no stored procedures, no sub-selects (ie no "SELECT * FROM users WHERE user.id IN (SELECT userid FROM admin_users)". But it *is* free, and it *is* included in many web hosting packages

You won't get a decent site done in your spare time in four weeks. There are issues you haven't thought about yet. For example, have you thought of including an admin interface for the people running the site to delete/edit users, get stats, change passwords etc? Of backing up the data and being able to recover it?

Clients, eh? Who'd have 'em...