You will always spend more if you build a bike up from parts rather then buying a complete bike. Complete bikes are available over the internet and while some of them aren't super duper, they're good prices and if you replace parts as they wear out, you can slowly build yourself a good bike while still being able to ride it. I'm not going to recommend a particular bike because it's not a market I take a lot of interest in, however, you will find regular, ongoing discussion about the cheap end on the[url=http://www.bikeforums.net/forumdisplay.php?178-Singlespeed-amp-Fixed-Gear&s=44db50faff6b03f1ecac533a10e44a52] Singlespeed & fixed gear forum of the American Bike Forums.
I wouldn't buy a new frame unless you know exactly what you're after and to be honest, you don't, not yet though you will in a year's time. Buying a frame alone only works if you buy a good quality frame because that's the heart of the machine - it's a big component to replace, hence the advice above to buy a complete bike.
Another excellent way of going about it, is to get an old road frame, one that you can ride (and so test how it fits and works for you) and then gradually convert it, much as I did the Europa. You can keep the bike on the road that way, enjoying riding it, while you save to buy good parts.
My Europa started as a basic conversion with a track cog screwed onto the road wheel (suicide hub).
Some while later, I bought the wheels, cheap wheels but good wheels, not rubbish.
I sourced some good brake levers off ebay
At this point, she was still wearing two chainrings ie, I hadn't touched the cranks. Eventually I removed the surplus chainring. I've only just got around to replacing the cranks and last month, fitted new, dual pivot brakes to replace the diacompes from the 80's. The whole conversion has taken about 5 years and each step was taken at a time when I could afford to buy good parts.
Cheap deals are rarely an overall, good option - you do get what you pay for.