i'm building one right now. i had the frame, slide, and barrel all fit by a gunsmith. all of this is possible for someone with minimal tools and an intimate understanding of the gun, but they are the major components of an accurate gun, so i wanted it done professionally. it is still requiring some fitting of other parts like the grip safety, thumb safety, trigger, etc, but this can all be done with a file and some sandpaper.
if you are looking to do something easier for your first go around, start with a basic mil spec 1911 and just replace all the internals. that way, you know you have a fit slide, frame, and barrel. you will gain a more intimate knowledge of the gun, and learn some basic fitting, without having to tackle the hard parts.