I can't this hasn't been recommended yet, but what about the American Dlx Jazz? They are even more versatile than the American Std. They run $1300 from MF, but you will be able to buy one from a GC or other dealer for under $11-1200 realistically (mine was $900 brand new with no defects). I mean, they can do the regular Jazz bass tone(s) that everyone knows and loves (just cut a hair of treble from the EQ), but they can do so much more. On top of that, they are lighter and use better components than the Am. Std. Jazz (except the bridge). Best gigging bass that I've found so far.
A good P/J style would get an honorable mention though...maybe the Tony Franklin Fretted Precision?
A good P/J style would get an honorable mention though...maybe the Tony Franklin Fretted Precision?