Try a Remington 700 with a factory Synthetic stock in 25-06
and a good scope, like a Leupold 6.5 to 20 or something similar.
The Remington trigger is excellent, but is shipped heavy , turn the screws to a 1.5 or 2 lb pull.
Good enough for Bambi, sheep, groundhogs, coyotes,
and is legal for year round use in Ontario,
Calibers OVER 7 mm , like 308 are only good at the range , or in big game season.
...
Low recoil, nice bullet selection for explosive expansion on varmints, or controlled soft points on bambi
Extremely flat shooter
http://www.shootingtimes.com/ballistics/25_06_remington.html
25-06
If you sight 2 inches high at 100, you are still within groundhog vital area at 300 yards so your range estimation skills don't have to be spot on.
I have used a friends and hit a 500 ml waterbottle at 300 yards.
the rifle could do it all day, but I was the weak point, seeing my pulse move the scope reticle each heartbeat.
If you want to go custom, you can do it all, bit by bit later on this platform.