If you’re looking at Fender, I’d encourage you to get a precision bass over jazz for those styles or if you want a bit more tonal range a PJ (precision neck pickup and jazz bridge pickup).
How much do you want to spend? Are you open to buying second hand?
Willing to spend as much as necessary for whatever constitutes a "pro" instrument (imo a pro instrument is one that has gold standard tone and won't get in the way of virtuoso techniques). Obv this varies from instrument to instrument, like for the string family that's around $3.5k, guitar around $1.5k, and other stuff like banjo $5k or god forbid woodwinds, bassoon at $10-20k.
Fender not a requirement, just want relatively understated styling.