RE: .243 or .308
Ditto to Retrieverman if you have to choose between a .243 annd .308. However, for what you have posted, I would look at the.223 or something comperable, and there are a ton of em.
For plinking well beyond .22 Long Rifle, I bought a 17 HRM and love it. 2,550 fps and it is an honest 150 yard plinker; but it hates wind, so if you shoot in a windy area, it is a terrable idea.