I bought a Classic Vibe 60's Precision, threw Rotosound flats on it...and it's a great bass. I'm using that one for blues/classic rock/country.
I'm thinking about trying out the Squier CV Jazz bass or the VM Jazz bass (or even the Fender Classic Series 70's Jazz bass model) to see if the neck size would work for me.
My problem is that my hands are too big for most Jazz bass necks. I've had two Jazz basses in the past and I ended up having fretting issues (fingers would "miss" notes and such)...which led to my selling them in favor of P basses.
I might have to "make" a new J bass with a P neck if I can't play one off the shelf.