The Bass thread (funk, Paul McCartney, guitar)

[ElephantSack]

If I may interject...

I grew up playing a Mexican-made Fender Jazz, and it was an all-around great bass, although it was my first, I didn't take very good care of it, and it was eventually stolen from me But mine was made in the early 90s, so that might also have something to say about the quality. I've never been big on precision basses, but then I've never owned one, either.
I was also going to recommend Ibanez for a starter upgrade. They're lightweight, easy to play and have a pretty wide range of tonal capability, and they're relatively inexpensive. Some of them are straight up cheap, but you are looking for an upgrade, after all. Same story with Peavey.
Schecter makes some quality basses. My weapon of choice right now is my Custom Stiletto 5. They're mostly mid-range to high end as far as price goes, but if your heart is set on a Fender, you might want to go with that, but you should also decide whether or not to side with a passive electronic set up or an active set up.