I don't think you'll find any dive boats to be all that crowed that time of year outside of Thanksgiving week. I happen to like bigger boats in the winter since the wave action can be more intense than in the summer, though I've experienced some pretty calm conditions in November. The marine conditions will probably be pretty similar from Key Largo down to Key West. In you want a true six pack operator, then your ticket is Quiescence in Key Largo. I've been out with them a few times and they seem to be a good shop.
Conch Republic in Tavernier is my favorite shop because the folks that work there are great. They have a small Island Hopper but mostly use their big Newton 46 boat, which is really stable when the waves kick up. Even on Labor day weekend, the boats weren't too crowded. In fact I had several dives where there were only two to four of us on the boat (we used the smaller Island Hopper for those dives). I also did 3 dives with Silent World over the same weekend on their Island Hopper and it wasn't too crowded either. Last weekend a friend and I made six dives with Rainbow Reef: they have big Newtons but their boats were crowded as can be. They do have a nice staff and if you're looking for a free guide, they offer one (we didn't use guides). No other shop that I know of provides guides for free.
Key Largo and Islamorada are really good choices for newer divers. Lots of shallow reefs, a handful of deeper reefs and both shallow and deep wrecks.
