Re: J-bass? P-bass? PJ-bass? What's good for a begginer?
I think basic, one-pickup basses are great for beginners. Something like a Classic Vibe P or Bronco. Not only are they easy to figure out and non-distracting, but there also isn't a lot that cannot be done with them, if you learn to use technique to squeeze the most out of them. Jazz basses and active basses are more complicated and distracting for someone just learning to play, and they do some of the "hard stuff" for you, so you may not be forced to learn how to do it with your fingers.
That said, the bass you learn on doesn't matter all that much. Despite my recommendation above, I learned on a '77 Music Man, an active, fretless bass. That kind of bass is pretty much all I played for 20 years before discovering the beauty of frets and passive pickups in the form of a standard vintage-style P around 2008. I learned on that Music Man not because I really chose it, but because it's what was around (my dad's) when I learned. When I got my own bass in '96, I simply chose one very similar to what I had been playing for eight years: a G&L L-2000 fretless. Once I discovered frets and passive pickups, I did not look back. I still have both those active, fretless, "techie" basses, but I have not played them more than a few hours a piece since picking up that P. My thinking was, "Where have you been all my life?" There is simply nothing like a good P-bass IMO.