A 19 isn't going to be the most competitive gun in any division simply because the sight radius is too short.
That said, unless you're trying to win matches, USPSA is mostly about developing your skills and making yourself a better shooter. A 19 will do just fine for that purpose. Shoot whichever division you like(limited if you hate reloads), and just focus on improving your skills and doing a little better each time out.
If you ever decide you want to be as competitive as possible, invest in a gun that fits the division requirements and gives you all the advantage you can get. A G35 or G24 would be ideal for limited(or a 2011 if you want to go down that road), and a G34 is optimal for production. For either case, you'll probably also be spending $200-500 on upgrades to get a gun that is truly competitive with what other people are using.