There're lots of basses that'll cut it OK. After having been through a variety of instruments, I've recently admitted that the simplicity of P and J basses is very effective and versatile. I would look for a used P bass made in Japan or US. I've found a couple, albeit a little goofy looking, but killer playing, Japanese Fender Foto Flame P's for around $300 each. Great tone and useful in many styles. These are from the mid 90's.
Good luck.
p.s. two of my favorite bass players were/are Elliott Smith and Jason Falkner (both primarily guitarists, but keyboardists and drummers as well)