You could set up on one of those powerlines up at camp and take a pretty long poke!
Since you said you don't plan to hunt with it I would look on the lighter side. It'll be cheaper to load, and easier on the shoulder.
Lots of people shoot the .308 to a grand. Although it's kind of a "boring" choice.
The 6.5s are popular.
Lots of good options available since you handload as well.
-Jake