Before you buy a "F" bass try a few others. Having owned both the P & the J be cautious most of them don't sound as good as Jaco's. In fact I would describe the P as an electric plank, one tone only and my J hums under certain types of lights irritatingly. For a bass that doesn't cost an arm and a leg I suggest you try a Spector Spectorcore fretless, has the advantage of a Fishman piezo in the bridge. The old Yamha TRB is similarly equipped and that offers a useful alternative sound palate. Pino Palladino says he adds a little chorus to fretless to give it his distinctive sound and that is certainly pleasant. You may also want to experiment with different strings, wire wounds will give you more bite but they churn up the surface of the fingerboard badly. (Jaco painted his finger board with epoxy glue to harden it). If you can afford to make sure the fretless bass you choose has an ebony finger board, it's much harder wood than rosewood and produces better sustain. Flat wound strings are less damaging to the fingerboard, but generally seem to have less tone than wire wounds, although I am sure that now loads of flat wound string aficionados will detail the benefits of their favourite string make. I do use flats myself but find that a pre-amp equaliser is needed to colour the sound to my taste.
Good luck and have fun.