Upgrade TO a 19"? I hate to think what you must have now
Can you afford a 22" widescreen instead? Lots more pixels there.
You want a 5 ms response time (or 2 ms, even better). And, ideally, you'd be allowed to check for dead pixels before buying, or you'd have a return policy that lets you get a full refund if you ask within 2 weeks.
There are other things like DVI, viewing angles, panel type, etc - but I'm assuming your budget is low and they're not that important.