I think the M1 or the M1A are your best choices, based on your description of what you are looking for.
I own a 20" Colt HBAR AR-15, my son owns a very high grade Garand and a equally sharp companion M1A Scout. My HBAR is very accurate out to 300m...but in my case only because I mounted a Trijicon compact 3x24 ACOG on it. Otherwise I'm too blind to hit a damn thing at that range!
My kid is deadly accurate out to 300yds with his big bore rifles with their iron sights. When we shoot at most rifle matches here, he is usually the only one shooting a dinosaur...most of the rest of us shoot .223cal 'poodle poppers'.
Either one is a fine choice, but in my humble estimation, the Garand is the finest shooting rifle ever made...followed closely by the M1A. Don't get me wrong, I prefer my AR...but those other cannons are real mens' rifles.
BTW, I believe that the favored rifle of the SEALS now is the match grade synthetic stock M1A, with iron sights. They use a wide range of weapons, but for just rifles, I think its the .308 M1A.