With regard to "building" a bike:
- If you are going to *convert* an old bike, and doing so to save money (and for the experience), make sure you don't upgrade many of the parts. If you start upgrading all the parts, the price of a conversion will quickly start to look like the cost of a new beginner track bike. If you want to convert a bike for the purposes of fixing it up or making it look nice do so knowing you *aren't* going to be saving money. You could do this cheaply if you have nice spare parts lying around your house but if you are new to cycling this likely isn't the case.
- If you are going to build a new bike *from scratch*, the only reason to do this as a new cyclist is for the experience of building and maintaining your bike. Inevitably, building a bike from scratch will exceed the cost of a stock beginner track bike, PARTICULARLY if you want nicer parts than you would find on a stock beginner track bike. I personally think that experience is very very invaluable. Just know that it will cost you.
If you are not interested in the experience of building a bike, and can afford to spend a small sum of money, I recommend just getting a new beginner's track bike. If you spent $100 on new wheels, $20 on a cog/lock, and another $10 on a chain - basically the bare minimum of parts you'd need for a road-to-fixed conversion - you'd already be sitting at $130 (not to mention tubes/tires), plus the cost of the conversion bike. So if you were willing to wait one more pay period and drop an extra $200, you could get a really nice beginner's fixed gear bike.
But like I said before, if you are doing it for the experience of working on and maintaining a bike ... you can't really put a price on that. Just know your intent in doing it.