Isn't groundhog hunting an "every now and then" sort of shooting? The population densities aren't all that high, compared to prairie dogs. Seems to me a bolt-action rifle would be more practical.
You'd commonly be shooting from a "cold" barrel, so a heavy-weight target-type barrel wouldn't be important. A light sporter should do just fine. The most important factor would be learning the trajectory provided by your combination of rifle and ammo, and then being able to judge range. (Or use a laser rangefinder.)
As far as optics, 9X should be adequate, although 14X would allow a bit more definition. 3x9 or 4-ish x 14 would do...
I'd figure the .223 to be practical out to 300 yards on groundhogs, based on what I've read about them. The .22 Hornet and .218 Bee have killed many a groundhog, out to around 125-150 yards.
The .223 will definitely ruin a coyote's day, out to maybe 200 yards for "clean kill". (Sure, you can hit a coyote farther out, but it might not be good enough that it's an ethical, quick end.)
FWIW, Art