What Bike?

For your size and weight you need a full size bike.

To keep in your budget you will need to buy an older bike and it will probably need to be a 2-stroke. Keep in mind that bikes come in several basic varieties: "Off Road" and "MX" and a mix between the two.

The "Off road" bikes are way cheaper, usually four stroke. They have a smaller frame with a significantly lower seat height, which appeals to women and short men. They have significantly less suspension travel and in general are heavier and less capable bikes. Great for putting around on trails but you don't want to take them to a track.

The "MX" bikes are built for racing and usually don't have any frills, such as headlight or a kickstand. They have high performance engines which can be tempermental.

The "Mix" bikes have the high performance engine, long suspension travel, frills such as electric start and a kickstand. They are just a little bit heavier than a MX bike (due to the battery and electrical system) and will typically be the most expensive.

Examples of these bikes. Yamaha:
"Off Road" is a TTR-230
"MX" is a YZ-125, YZ-250, YZF-250F, YZ-450F
"MIX" is a WR-250F, WR-450F

Any of the big name bikes would be fine, but stay away from any "no-name" specials. A 20 year old Yamaha, Honda, etc. will still have parts easily available and provide more years of service than a cheap no-name bike.

I would recommend something like a Yamaha YZ-250. If you survive the first couple of rides you will enjoy such a bike for a long time. It has the power to get you into a lot of trouble, however.

A YZ-125 would be a good bike to start on and would serve you well but you might yearn for more power once your skill increased a bit. The 125 will be cheaper, easier to start and generally easier to ride. Until you start tackling big hills. You can climb then on a 125, it just takes more skill than it would on a 250.

A Yamaha TTR-230 would be a great bike to learn on, very inexpensive, four stroke but you will outgrow it very quickly. I am pretty sure that a decent four stroke will be out of your price range.

Save a little of your budget for the necessary safety equipment.

A helmet is a must.

Goggles are also a must.

I highly recommend a decent pair of boots. They will save smashed toes, twisted ankles and burns to your calves.

Gloves are a really good idea.

Knee pads and chest protector go a long way towards helping you get back up after a fall.

Keep in mind that you also need to be able to transport this bike, so if you don't already have a truck then you will need a trailer.

Good Luck!

Rod