Converting a road bike is not a bad idea if you're not 100% sure you want to put a lot of time and money into fixed gear cycling before trying it out for a bit. They can generally be had cheap, then pick up a cheap set of wheels from velomine.com, which you can then swap onto a build or another bike if/when you decide to upgrade.

Building a bike from scratch is going to prove to be more expensive, even if you use lower-end parts.

The Kilo TT is so highly recommended because it comes complete and is a great starting point for a beginner. It comes with decent components and nothing needs to be replaced immediately.