I think you'll probably want something with a Jazz pickup in the bridge (perhaps a tapped humbucker, for even more versatility), and a P bass pickup in the neck. The wood on a bass really makes a difference; Warwicks tend to have necks and/or bodies made from Ovankol, and i recently did a neck conversion from a maple warwick neck to an ovankol one, and it brought out a lot more low-mid growl in the sound, which the maple just didn't have. That said, classic bass sounds have been done with P-Bass (Steve Harris) and Jazz (RAtM), but they are quite distinctive, much like a single coil versus a humbucker.