It really depends, there are many schools of thought on this.
Personally I think if you're responsible and level headed you can start off on an older 600 (something like an early to mid 90's Suzuki GSXR or Honda CBR series 600's) they are solid bikes and are pretty cheap and easy to maintain and keep up. Stay away from newer fuel injected 600's, they are a lot quicker and will get you into trouble pretty quickly if you're not careful.
Don't buy new, stats show you're going to put it down and nothing is worse then laying your brand new bike down.
If you find that you don't want a 600, look at the Suzuki GS500F or Kawasaki 500, those are great bikes that get great gas mileage, they aren't dull either, they'll make it to 90 mph. If you look at GS500, look for a non-F model, those are naked bikes so if it does go down there will be less to scratch, although you'll lose some of that sports bike look IMO.
Try to get someone who knows motorcycles to go shopping when you're looking at something used, hold out, there are gems out there and don't fall for the first bike out there. Check the vin number on the frame and have the owner ride it to make sure it rides straight, look for any leaks or knocks. Check out the condition of the chain, the condition of the tires and make sure it shifts into every gear without issue.
Check the forums of the respective motorcycle, they will give you a ton of information on possible bikes that you're looking at as well as known issues.
That is all I can think of, I'll post some more info.