You really can't go wrong with a P or a J bass.
If the bass role in most of your music is more "fundamental"... where the bass is primarily supportive (Pretenders, U2, Green Day), I think the P is the better choice.
Sits perfectly...
If the bass role is a little more featured (Rush, RHCP), the J will give you a little more articulation.
Another bass you might want to consider is the Stingray.
Also records well...
The SR has an aggressive character... which you may or may not like.