I'd get a P-Bass, string it with flats, and run it through an SVT rig.
But that's me. What you should get? Only you will know. Go play every bass you can get your hands on and play it through a rig similar to your own (or bring yours along if the stores don't have your rig) so that you can get a better idea what it will sound like for you.
Trying out basses through a rig that's nothing like yours will not give a good idea as to it's sound when played through your rig. The amp/cabs can really change the tone of a bass, so when you buy one and bring it home and play through your rig it may sound entirely wrong for you. Also, the choice of music you selected still tells us nothing except you want a variety of tones. For variety in tone, try an active bass with two pickups and either a blend pot or dual volumes (not just a switch that goes full on one or the other, or both full on) that also has a good onboard preamp with a three band EQ.
Asking here what bass you should buy, is like asking us what girl you should date. Lots of opinions that won't make one bit of difference in your level of happiness with your choice.
