As a starting point, a clean intact barrelled action is nice to have.
Before committing to the project, it is a good idea to research the availability of the parts you are going to need. Most anything can be found, if you look long enough, hard enough and are prepared to spend enough. Might not be practical though.
I made up a faux 1903A4 sniper rifle, starting with a badly bubba'd 03A3. A friend here helped me with the stock and handguard. The small metal bits were easy to find. I had a scope altered bolt from a Midland 2100, commercial base and rings, and a 330 Weaver scope. Looks good, shoots great, cost was very reasonable.
If you want to bring tears to your eyes, try to put a M-1 rifle together from parts, starting with one of the very inexpensive receivers. A C No. 7 Mk. I .22 is in the same category. Receivers are cheap. The only part that is.