There a lot of good bikes out for starters. One of my favorites is the Nighthawk 750 by Honda. Some others have pointed out some great bikes as well, such as the GS500. I’d shy away from 250’s for several reasons, but the main reason is that for a person your size, you’ll need a bike that can move your mass a little more effectly. That’s why I like the Nighthawk; nice torque without being overly horsepower packed and peaky.
A word of caution on shopping cc’s; displacement doesn’t neccesarily tell the whole story on how powerful a motorcycle is. For instance, I’d NEVER reccomend to you to get on a 450 Motard, despite the fact that it’s “only” a 450. A 650 Ninja, SV650 Suzuki or M620 Ducati are all reasonable motorcycles for beginners with air/oil cooled motors with ~60 hp. On the other hand, the FZ6 or any faired water cooled multi-valved 600 would not be what I might reccomend as these have ~100hp and more and CAN BE a little more challenging to learn on.
$3K is a nice price point!
Ride safe!
Ironbutt 270