Building your own fixed gear bike is really satasfying. I don't mean to discourage you, but you might spend more than $250 once you get hooked. Between tools and new parts it can get relatively expensive, especially if you want something of quality.
You can definitely get a decent bike together for around $250, but if you want to build a bike that will keep you happy for a long time, throw in a couple more dollars from the start, you won't spend as much later. Have fun!