new rider, new bike help

I am very new to the motorcycle world and I want to be buying a bike soon. I have driven a moped around as well as a honda 90. I want to upgrade to a bike that I can ride alot more seriously. I am thinking about a Kawasaki ninja. I would like a 250 because of the fuel, but after some research I think I need a 500. I am about 240 and 5'9".
Does anybody have some suggestions. I want to buy a used bike somewhere around $2,000 and I want it to have good gas mileage. If somebody has anybody advice about good beginner bikes, or if a 250 is too small I would appreciate it.
Thanks a bunch,
Tim

I think you might find yourself wishing you had gotten a bigger bike than a 250 very quickly. I'd shoot for a 650 cc or something like that, but that's just me.