I’m a new rider with barely 1000 miles under my belt so take my advice with a grain of salt.
The 500-650cc standard/half-faired sportsbike class looks pretty strong these days. As a new rider I’ve been looking at bikes that size. I don’t think I need, or can handle, any more than what these can dish out.
Yamaha is coming out with the 600cc FZ-6 for 2004, Suzuki has the SV650, 650 Vstrom, and GS500F. The old GS500E is supposed to be a good beginner’s bike. The Yamaha Virago (250cc) or other small cruiser might be good for your height.
The Kawasaki Ninja 500 is a good beginner’s bike.
Honda has the Nighthawk line.
Used Nighthawks (250 and 750), Ninjas (250 and 500), and GS500Es abound, so you shouldn’t have too hard a time locating one.
I would argue against getting a bike that’s too light (for instance the kind I have, a Yamaha XT225) because you’ll be buffeted by wind once you get going faster than 55mph or so, and that’s not a good feeling. I guess it depends on where you’re going to do most of you’re riding, though. I ride twisty mountain backroads that are in various states of repair, most of which have no lines and are barely wide enough for two cars to pass, so my small, light dual-sport is excellent for that. It’s not at all good on the highway, so next spring I might have to add a more highway-worthy bike to my stable if budget allows. Darn. 
Hopefully you’ll be able to ride where there isn’t a lot of traffic. I love riding my motorcycle and without the pressure of traffic it’s even more enjoyable.
BTW my stupid newbie mistake has been not shifting all the way down to first when I stop. I may think I’m in first but I’m really not, or I just forget and I take off and the bike stalls and I have to fumble around like an idiot re-starting the bike, getting down to first, taking off very cautiously, you get the picture.