As others have noted, headspace is critical. I should have been more specific above and advised that when putting a previously used USGI barrel and used USGI receiver together the headspace usually is OK unless one of the USGI parts is worn out (or monkeyed with). Both of the parts were originally manufactured and assembled separately but to USGI standard specifications. Sorry for my oversight. BUT, you are putting a USGI barrel on a COMMERCIAL receiver so you have no idea what the resulting headspace will be. It is just as bad, if not worse, to have too little headspace (short chamber) than it is to have too much headspace (long chamber).
If you don't already have the receiver wrench, barrel block and headspace gauges they will set you back about $150, so you may want to consider just sending it to a competent gunsmith to do the whole thing, including finish reaming the chamber if necessary. If you have to finish ream the chamber to get proper headspace it could cost you about another $100 to rent the reamer, and I hope you are very patient and mechanically inclined.
Not trying to discourage you but only to make you aware of reality. Good luck.