Sorry to be so pragmatic, but let's consider what you want. Do you want a Jazz-style bass that feels good, plays good, sounds good, and looks good? (yes obviously) So, if this is your 4 goals - it becomes easier to break down.
1) Feels good; This is custom baby - tell (the luthier) what you want. Do you want a typical Jazz bass? Or is there something you'd like to ergonomically change, to alter, or to emphasis based on a Jazz-style bass?
2) Plays good; Again, think custom - what would you like it to play like (be specific as possible) thin neck? fast neck? fat neck? thin frets?, fat frets?, no frets?, 1960 J?, 70's J? (mostly a neck issue)
3) Sounds good; What pu's?, what electronics/pre-amp?, what wood?, what strings?, what nut?, what bridge?... (in that order) need addressing. Maybe you'd like 3 pu's (like a Strat) This is the world (of custom) available to you.
4) Looks good; I know, it HAS to look good. But sometimes if you fulfill 1-3, it ends up looking great! Enjoy fancy woods/laminates, but remember it usually has very little to do with the tone, regardless of what you've read. (unless it's focused on the neck, where most all your tone comes from.
Post your journey.