If there's a store nearby that you can go to, do that. Seriously. Try out the Jazzes and the Precisions and make sure you also try out *every thing else in your price range*, including (especially?) any used basses. Buy what feels best in your hands.
And don't be afraid to go in there not knowing how to play. That's how I bought my first bass and the salesman I talked to was not only pretty cool about it he was also pretty helpful. I ended up with a Jazz and have now owned three of them
If you keep up with it for a while you'll have one of each anyway and, yes, I *do* have a Precision now as well.