$2k limit, prefer no shaft drives, must fit comfortably-I can do sport/supersport bike fitment as well as most mid control bikes-forward/cruiser controls don't agree with my legs, has to be able to 75mph plus without struggling on long upgrades....
I'm sure there is more to it then that, but immediate area CL searching can only go so far......
I know a lot will say a dirt bike and I have to agree, not to mention dirt and grass are much softer to land on 
Heh... Street bikes only. Dirt ain't as soft as one thinks.....
Better than tarmac in most cases, at least in my own personal experience.
Idk the prices but maybe a katana 600?
Lots of people will say "get a 250" or "smaller is better" or offer their specific bike of choice but - I'd say get something easy to operate that fits you. Pick any reliable japanese standard from say 1990 forward in a size that fits your ergos and does not seem too heavy for your personal strength. Having to wrestle a beast in slow speed situations will keep you from learning to maneuver easily.
Check that it does not shake so much you can't clearly see in the mirrors. Thumpers are sweet - but if you can't see behind you in traffic it's a bad learning tool. No matter how much motor you end up with... make sure a smooth throttle and wide powerband are included. Something you can easily modulate. It is less important to artificially limit the potential by buying a itty-bitty motor than to be able to control what you've got. If you sneeze and find yourself floating in mid air looking at the tail light... too touchy for a noob
"Dirt bike" isn't a bad idea... the mid size dual sports usually have upright seating and good low speed maneuverability with enough zip to run down the highway. Although... they are very buzzy unless you can afford a parallel twin.
Ranger50 wrote: Heh... Street bikes only. Dirt ain't as soft as one thinks.....
It's not the dirt that hurts, it's the landscape. I'm not sure who put all the trees and rocks in the woods but they are really painful to land on.
Well, if you are interested in a minor project (tuning carbs) I have a 98 GSXR 600 for sale. It is under your cap and decent looking bike. It "only" makes 95hp and if you keep it under 8K rpms decently docile. I am up in Central MO though. That is like 9 hours from E KY. Oh well.
Why no shaft drive?
I'd rather be riding than working on it.
GS500. Your stated budget should get you a very nice one. In the off season nice ones can be found in the $1200 and under range.
A lot of GRMers call the SV650 the Miata of motorcycles, they can be had in your budget range too. 
Dual Sports tend to be very forgiving to beginners, if you can physically handle the seat height and top heaviness, larger displacements will do highway speeds, but will be very buzzy unless it's a twin.
Just about any UJM type from the late seventies through mid eighties under 750cc could be a good candidate too.
Play around with www.cycle-ergo.com to see how you'll fit on various choices.
Honda vfr interceptor, Yamaha Radian, Suzuki sv650...
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