First thing to do (other than taking a rider training course) is to sit on the bike to see how it feels. If you have a license, a dealership may let you go for a test ride. Feel out the bike, it is the best way to see if it is right and a good fit.
I’m about 6′, with a 32″ inseam and when I sat on a 2009 250R I found it to feel a little small, but not uncomfortably so. Although the Ninja has a great resale value, and if you buy used you can usually sell it for about what you paid for it.
The Hyosung 250 are comparable to the Ninja, but have a little more room. Although, the 2009’s are carbureted, the 2010’s are injected. There are a couple of major issues with this company however, they are new in the US market and because of this have little support. Also, the build quality is not quite as good as the Ninja, but is getting better each year. Another issue I have is that unlike the Korean cars that came out about 15 years ago, Korean motorcycles are NOT half the price of their competition.
A Dual Sport might be a great choice also. Nimble, light, roomie and off-road capable, they make for a fun ride. The problem is that if you get a used one, it may be a little beat up. Like Craig suggested supermoto/enduro bikes, which are basically dual-sports with street tires.