Always the Brainer, Skinner and Battlebabe, because c'mon.
Most of the Hardholder, Hocus, Operator, Chopper, Maestro D', in about that order.
Maybe the Savvyhead, Angel, Gunlugger, or Driver, depending on the setup.
Sometimes other playbooks, if people are specifically into them or they are particularly appropriate.
Never the Touchstone, because eff that thing.
"Depending on the setup" includes whether or not it's a one-shot, and then also what sort of apocalypse everybody is into. I'm a lot more likely to limit the playbooks for a one-shot or when introducing the game to a new group. Savvyheads and Angels are good playbooks to remove for one-shots, in my experience. And of course the Driver/Chopper books are an easy one to include-or-not depending on one's vision of the setting.
But with my regular group, we've generally played enough AW that 'which playbooks get offered' becomes a sort of group decision-making process: all the basic books start on the table, and then someone might be like 'I'd like to try a game with no Angel' or 'maybe there's no Brainers out here' or 'Can we maybe have a Quarantine, if everybody's on board?' or whatever.
I never think of it in terms of how many players/how many books, though I feel like there should always be significantly more books than players.