I was about your age when I bought my first bike. I wanted a new bike, but the first thing my dad asked me was where I was planning on getting $5,000. I ended up saving my money and getting a 1975 Suzuki TC125 for $100 on ebay. That bike taught me how to work on motorcycles and how to ride. You WILL break stuff. You WILL crash your first bike (if you are like me, scratching a new bike will make you sick). Work your way up to a nice new bike. Your friends will make fun of you for having an older bike, but if you learn like I did, you will never pay some guy $50 an hour to fix your bike.
I sold that first bike for $900 and bought a newer, bigger bike, then sold that one for a 2002 kx125 then sold that and bought a brand new Honda CBR600RR for the street.
Look for something in the 125-150 range. Make sure it starts good in the cold and shifts well through all gears. The make really doesn't matter, just make sure you can find parts. Get a CLYMER manual for it. Have fun!