Help....

I have a basic problem with someone whos primary qualification for a bike is how fast it will go.

Just about any bike will go fast enough to get you in way over your head.

I really do not recommend riding a dirt bike on a trail that allows you to crank the throttle open and hold it there. I avoid those trails because it is far too likely to encounter a large, four wheeled vehicle doing the same thing in the opposite direction. If you manage to dodge the first one and are then blinded by the dust you are likely to get run over by the second guy he was racing.

If you want a real thrill and to demonstrate your ability try going fast on a trail where you really have to handle the bike. For this you not only need to know how to ride but you have to have a bike that has a good suspension, is light and nimble. If all other things are equal more power would be nice but raw power is a poor substitute for a good suspension.

That said, based on your size, desire and budget I would recommend a 250cc 2 stroke MX style bike. Something like a Yamaha YZ-250. You shoudl be able to pick up a ten to 12 year old bike in your price range. It will have plenty of power, certainly enough that it won't be the limiting factor.

Rod