Though I agree wholeheartedly with 4stringfarley's response, I realize that that may not be a particularly satisfying answer. So I will add the following:
1. The ABSOLUTE MOST important aspect of a bass is that you really like it. Ideally it should make you want to pick it up and play it every time you see it, because what makes you a better player is practice.
2. The Precision is a legendary style bass for good reason tone-wise. However it has a chunkier neck than a Jazz, which makes some with smaller hands more comfortable with a Jazz.
3. My first bass was a J style, which is something I do not at all regret, but an important aspect of learning is the differences you can make with just your hands, where you play on the string and how hard you pluck (or pick). A Precision will force you to learn these lessons because you don't have the option of mixing in a bridge pickup (unless its a PJ).
Hope this helps you with your decision.