I have this 1984-1987 MIJ Jazz Bass. I got it for $150 from a some pawn shop. It only had 3 strings on it, but I guess hanging from the headstock kept the neck from warping (thank god). I know very little about basses, but I know this for sure. This thing needs a new nut. When I put new strings on it, they rested on first fret. I shimmed the nut, but that only allowed enough relief for an annoying buzz to appear.
Q1: I am familiar with how to slot nuts on a guitar, and may I assume it is similar with a bass?
Q2: What kind of nut is desirable on a bass? It has brass right now. Does bone provide a "better" tone (if they make bone for bass), or should I stick with brass?
Brass nuts are not tonally transparent, so it's an aquired taste. Some people love the clarity, and some people hate the tonal difference when compared to that of a fretted note.

If you go brass or bone, nobody's going to hate you for it - however, brass nuts on a Fender is unusual.
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I was looking at a used Warwick Vampyre LTD 5'er for about $200. I went home to grab my wallet and came back and some jerk with an epic beard got it already..