I much prefer .308/7.62x51 for performance reasons to .223/5.46 (including range, knock-down power...). However, give the high price of military ammo right now, "little" bullets (i.e. .223/5.56) would be the cheaper way to go unless you have a great deal of money to spend or reload extensively.
ARs are typically cheaper than their .308 couterparts (FNs, M1-As/M-14s..), unless you're considering an AR-10 or similar variant.
If you're primarily concerned about shooting longer distances then perhaps you migh consider getting a 20" or 24" model AR and a nice set of optics to give you the best down range performance.
PS
I purchased my first Armalite AR-15/M-15 a while back and it is an amazing rifle. Don't be so quickly swayed by all of the Bushmaster zealots around here.