Yes the M1 Garand is a .30-06 rifle. It's little brother the M1 Carbine is a .30 carbine.
No, the CMP sells only semi-automatic rifles. The M-14 is a full automatic rifle that requires a class III FFL.
I would think that if you could find an M-14 it would run several thousand dollars - is that a low price? Here behind the lines we don't worry about class III weapons. Oregon is a class III state so you're good to go once you pay the tax and get the approvals.