Living in Indiana, I shoot a lot of ground hogs. my suggestion would be the 243 in a bolt action. I have permission to shoot hogs on some fields that are over 1000 square archers. Ground hogs over 400 yards are not uncommon.
But I have found it very difficult to get within a 200 yards of a coyotes with the flat land we have.
The 308 is a great round but the 243 will be flatter and with light varmint bullets the chance of rounds bouncing off the hard dirt is reduced.
I use a 6mm Remington which is a slightly higher power round than the 243. It’s so flat shooting that it can follow the curvature of the earth.
Although I don’t use it for deer (heavy barrel) I would in a second with heavier bullets. (120GR)
If you’re going to carry it on a tractor or farm truck then get something with a plastic stock and stainless.
The Remington 770’s a nice choice. And they do make it in 243.
http://www.remington.com/products/fi...model-770.aspx