Word on the street is that conversions usually end up costing more than buying a new bike, and can be a boat load of trouble trying to get chainline aligned, unless you have a way to get parts for free/work-trade. Unless you go with just singlespeed, in which case it's just pull off the unnecessary components and put on a freewheel...
This notion seems outrageous at first, but the cost builds fast when you start adding up the costs of new rear wheel or wheelset, cog and lockring, new chainring, probably new bottom bracket, new chain, new brake if your current wheels are 27 inch and you switch to a matching 700c, as well as any other associated maintenence/hidden problems that may pop up, etc.

But, all that aside, it can be a great experience and a wonderful way to learn about working with bikes and bicycle maintenance. I built a conversion myself, but I also had access to a bike co-op at which I could do work-trade for parts. If you don't mind going used, there are actually very few new parts that you need, and the single largest expense will be a new rear wheel.

Building a rear wheel usually isn't much cheaper than buying a new one already made. Even cheaper, take a look on craigslist and see if anyone has a wheel with a fixed hub in your area. Make sure to check it for trueness, broken spokes, bearing smoothness, etc unless you don't mind fixing these things yourself.

In my opinion, it comes down to the question of what you want the bike for and how you want it to come about. Fastest and cheapest (especially when you consider the time you would spend building one) the answer would be just by a cheap track bike... but if your goal is to take some time (a couple weeks to a couple months) searching for the lowest price parts and build a connection with a bike by building it yourself, go for the conversion!