If you build it up yourself you will almost certainly end up spending more than you think. Especially as you will need tools or be making several trips to the bike shop for installation. The up side is that you will get to pick out each one of the components, learn a lot and get the bonus points of being able to say "Yeah, I built that one up myself." Honestly though, if you're on a budget and you only want to change a few easily removed/installed parts I would buy a complete bike and swap out parts as the money comes in.

Oh yeah, also buying parts online tends to be a long slow process so don't expect to be riding that thing any time soon.