Look into the
Warwick Corvette Rockbass. They aren't as good as the more expensive ones, but they have good pickups, and are well-built and easy to play. In fact I'd say that Warwicks are by far the most "user-friendly" of any basses out there, exceptionally smooth, lightweight, with really good hardware and some good convenience features (like clips rather than screws for the truss rod cover and back panel).
They can cover a lot of tones just using the tone knobs alone. They don't quite cover classic metal, blues, jazz etc. as well, it definitely leans towards the more modern, tight & articulate side of things, so it might be good to have a P-bass or something on hand for that kind of thing.
Reading that site more, I think there are both active and passive versions. I have ones with active pickups, so that probably accounts for some of the high-output and brighter tones I can get out of it.
Really, more than guitar, bass is all about getting a good player and arrangement. A $200 bass can sound great on an album if the bassist is on top of things, but unfortunately there are quite a few guitar players (including me) who just want to play bass for their demos etc., and that's where things start to fall apart. I don't think expensive gear will ever save you in that kind of situation.