Jeph- I tend to disagree on the amp= tone when it comes to bass, mainly because, unlike a guitar, basses are generally played without effects. Not that you can't do it of course. For instance, there's an obvious difference between the woody tone of a Warwick versus the more rounded sound of a p bass. Also, just like on a guitar, the single coils of a j pickup tend to be a little less bass heavy and have more attack than a p style humbucker, while a MusicMan style pickup is a sort of comination of the two, but the frquency range is vastly wider than either.
That said, I think what you're looking for is a G&L L2000. It's made by Leo Fender, so it has that Fender vibe, only with vastly superior MusicMan style hardware and electronics. It's active/passive and has coil taps. DO NOT BUY A TRIBUTE! Also, the newer ones have gotten outrageously expensive. I think the older ones are generally better quality and can be picked up on ebay in the $500-$600 range. I had an '89 with see-through white finish for a long time that I loved.
With regard to amps, I agree, find what you like. Ashdwon, Ampeg, Eden, SWR etc. are the obvious names. However, with regard to the Behringer comment, I tested a Behringer 4210a, essentially a 2x10 with a 400 watt amp, and bought it. I had been playing on a huge rig with an Ampeg SVT 3pro, an Ampeg 1x15 and a Trace 4x10. The Behringer gave me the same power and clarity in a much smaller package. The speakers, however, are pure unadulterated garbage. I knew that going into it, so I replaced them with Eminences and got a hell of a versatile, powerful combo for slightly over $400. I sold my whole rig after that, and now gigs are much easier.
Just my .02.