I have 223, 243, and 270
the 270 has enough recoil (similar to a 308) that you dont want to put 100s of rounds downrange if you are shooting a hunting weight rifle. 243 has similar ballistics and less recoil to the 270. both of these will easily do 500 yards and with the 270 I can hit 18 x 18 steel at 700 no problem.
the 223 is the fun varmint/range gun, no recoil problem with putting a 100 rounds down range, no problem with popping steel at 300/400/500 but you have to be able to read the wind a bit better with this round than you do with the larger calibers.
My son is actually using the 223 varmint as his learning rifle for shooting at longer ranges, it is relatively inexpensive to shoot, accurate and fun.
It is your money and your call, I dont own a 308 so cant comment on that caliber. I can only say that if you are planning on shooting a lot of rounds in a session, recoil will become a factor. my 270 does not get near the range time of the 243 or 223, and the 223 gets a lot more rounds shot downrange due to cost and recoil.
Dave