It's a pain in the a$$, but very doable. Here's mine:

I won't go into to much about it because last time I spoke up I got a ton of crap over it. But I run fixed with 46/16 as my "magic ratio".
Bottom bracket is stock, crank set, stem and bars from ebay, wheelset from a friend, brake and lever from LBS, cog from Amazon.
I say go for it, use it as a beater and get a "proper" bike later. It's a fun project and you'll learn a lot in the process.
Good luck and keep us posted!