i just went through this. it can be cheaper in both directions, but theres plusses and minuses to both ends.

build it yourself and you get to see the bike unfold into what your vision is. its your personal expression and your personal taste that is shown in the final product, your parts, your custom build.

buy an off the shelf bike and you have a good solid factory built option, with all new nice parts, probably warranty.

i just kept checking craigslist until i found a bike then i pursued the seller and told him i was serious about buying it and to hang onto it for a day. he did and i got my bike complete - needed most new parts anyways to be rideable, but i got the whole thing for 40 bucks.

with a lot of elbow grease i re-painted the frame, kept the stock crank and arms, bars, stem, headset, seat/post and ditched the rest. bought new wheels, tires, tubes, grips, pedals, chain, and cog/lockring. polished a lot of the parts since there was rust on a few pieces and i came up with my first build/conversion. it was a lot of fun and i spent 150 on my wheelset, 5 bucks on my lockring/20 for the cog, 12 on my toe clips, 15 on pedals, 40 on tubes and tires, 5 bucks on grips, 10 bucks in paint, 12 on the chain, and 40 for the bike. so i built my entire bike for under 300, which is considerably less than some bike shops carry fixies for.

its really up to you if you would rather spend the time finding the right bike, or just buying one from a shop that has decent components already on it.