Being somewhat entrenched in the bass world at this point, I will caution you that it's less about versatility with bass and more about finding your spot, which a P bass generally does well. Opinions will of course vary on that, but I guess what I'm trying to say is that other than the occasionally bulky neck, I think the simplicity and it-just-works aspect of a P is what I would recommend to almost any beginning bass player.
I'm happy to hear that you're taking a her-first approach to this; I think it will yield way better results for both of you.