Ask your friend for honest feedback on his bike. Why is he selling it? Is he upgrading? You are new to biking as you stated, so are you certain of what you want yet?

I think you should find an inexpensive fixed gear bike and try it for a while before sinking a lot of cash into something that you might find doesn't suit your needs.

You can also go the route of converting a roadie to FG. Look for a nice double butted Cr-Mo frame preferably without downtube shifter bosses. Lots of threads here on how to convert. You can get a decent wheelset from Velomine or others for around $100 if you want to go that route.

Lots of options available to you. Also, remember, a $500 fixed gear is going to be an attractive target for thieves. Assuming you'll have to lock it up on campus at some point.