If it's a good quality frame, then it could be a fun project.
My recommendation would be to build a very simple GI spec 1911 using "drop in" parts only. Now even "drop in" parts will need some fitting, but if you keep things cheap and "drop in" then you'll find yourself with a working gun in a short time. What's more, you will have learned a little of the basics and then you can start upgrading the parts one by one to higher quality gunsmith fit one piece at a time. But to just start with a box of gunsmith parts having never built a 1911 before is a VERY rough way to go about a build and you'll likely become extremely frustrated and take to drinking a high volume of cheap booze in no time.
So start off with an inexpensive "Parts Kit". The parts are typically made by John Masen company. The parts are cheap investment cast parts, but that's not to say they won't work or hold up well; they will. Find an inexpensive slide and barrel and go from there. I really recommend going with the cheap stuff first (and again, it's not as if you're going to end up with a bad gun, it will be fine) so you can learn and learn on the cheap. Better to trash a 19.00 safety than a 75.00 one while learning; get my drift?
Sarco sells parts kits and they're a really good place to start. If you have problems finding all that you need, send me a PM and I can put you in touch with a friend who sells parts kits.