It depends on whether you want a "real" 1911 or a 1911A1.
There were several modifications to the 1911 to make it the A1. The mods were approved in 1927. (IIRC)
They included,
Frame relief cuts behind the trigger
The wide spur of the 1911 was replaced with a narrow one
Short trigger
(very slightly) improved sights
The flat Mainspring housing was replaced with the now common Arched housing
If you want a historically accurate 1911, you pretty much have to start cruising the gunshows for originals.
They're not that hard to find, and "beater" quality guns are not too expensive.
The Springfield Mil-Spec is a pretty close copy of the M1911A1, but even so, it's not exact.
Again, for a "correct" pistol, cruise the gunshows, the collector grade guns ain't cheap, but the shooters are reasonably priced and can be tuned up fairly cheaply.