My first build that ended up becoming my winter beater when I lived in the city, was a freebie '83 Univega Viva Sport. I think I did the whole conversion, including getting it painted by a friend for a bottle of Bushmills, for under $300. It was pretty close, though. If it's any consolation, the second fix I built was a true track frame that I managed to get a steal on through craigslist, and I put around $1200 into that one, so you know. In the grand scheme of things, you could have a pretty excellent bike for $300 bucks. One thing making it more excellent than buying a cheap but *new* frame, would be that you did everything yourself, learned in the process, and will much better understand what it is you may or may not be looking for in a bike in the future.
My two cents.