Ok, if you're looking for 250cc fast bikes, you'll be looking at two-strokes, such as Aprillia's RS250. Its a race-rep based on the 250GP bike. It's damn fast, kicks out 62 bhp at the crank, and weighs in about 140kg. Its often viewed as the best-handling bike in general, its really flickable. Top speed is about 130-140mph, and acceleration is about 0-60 sub-5 seconds. Drawbacks include I don't know how common they are in the US, and they require very careful servicing and warming up unless you want to pay $2k for a rebuild every so often!
Otherwise, you'll be looking at 400-600cc bikes. If you want a 'naked' (non-faired) bike, Yamaha's Fazer is a good, cheap strong bike with a decent de-tuned R6 engine. Others in the class to look at include Honda's Hornet.
If you want a race-rep/Sports bike, then there's the Suzuki GSXR600, Yamaha R6 and Kawasaki ZX6R. The Suzuki and Yamaha are a little quicker and lighter, but more pure racers; while the Kwaki has a more comfortable seat. All of them kick out 95-110bhp (crank),
should do around 0-60 4secs and about 160mph top speed.
The Honda CBR600 has two styles: a slightly softer CBR600F and a proper race-rep from the RCV, the CBR600RR. The RR is probably out of your price range, because its pretty new. The CBR600F, however, is a fantastic all-rounder. It's willing to do anything, from flat-out riding to comfortable cruising or 1000 miles in a day.
A 1000cc bike like the GSXR1000, R1 or Honda 'Blade (CBR994RR) is going to be putting out about 120-150bhp at the rear wheel, or 140-180bhp at the crank.
The GSXR1000 was recorded at 0-60=3.2 ,0-100=6.0 0-150=13.1. so its a real handful and so you're right, not really a starter bike.
My pick: 1st: CBR600F (or RR if you've got the money!), 2nd Suzuki GSXR600, 3rd Aprillia RS250, 4th Yamaha Fazer.
Good luck, if you've anymore questions I should be able to help.