Everyone here has brought up great points. The fact that you indicate you are on a budget, to me, is the main thing. If you are on a budget, you probably should look for a nice, lightly used bike and tear it apart and rebuild it. You will still be getting the experience and a lot of satisfaction in doing so.

It was mentioned above that you could buy a "donor bike". This is a great idea. In fact, right now I'm looking for a particular group and am just waiting until one comes up on CL. I'm hoping that a "tough to sell" size frame with a nice group comes up and I'll be able to get the components that I need more cheaply that way. Lots of the CL bikes were purchased with good intentions of riding to get in shape, etc. and they just sit in someones garage or basement. Five years hence, they need the room or they are tired of looking at a bike sitting still that should be moving and they dump it on CL.

If you have the time to invest, that's one way to go.

I recently completed a build of a track bike from scratch. I picked all new components, but bought them from probably 10 different dealers, including a road trip to a shop 2 hours away because they had a sweet deal. I love the bike to death because it was spec'd by me. It looks the way I wanted it. I still have lots of room to upgrade over time, but for now, it's perfect.

So I can understand why you want to engage in this effort. Just don't spend more than you have to in doing so.

Good luck!