I would say that you need a full size MX bike, so stay away from the "off road" models such as a Yamaha TTR-xxx, Honda CRF-230, etc. These bikes are great to learn on but as soon as you start hitting jumps they will be inadequate.
To get a decent bike in your budget I think you would need a two stroke as the four strokes tend to cost a bit more. A two stroke is a bit harder to learn on but I wouldn't expect a 20 year old aggressive rider to take long to get over the "hump".
So, for a specific recommendation I would go with a 5 year old Yamaha YZ-250 or a Honda CR250.
Don't forget to budget all the essential gear. Helmet is obvious, but goggles, gloves and boots are are also essential. I also recommend a chest protector and knee pads.
Rod