You are asking a cartridge to do two completely different tasks.
Groundhog (woodchuck) hunting can require some long shots, so a centerfire .22 like a .223 would be the best choice. A good groundhog rifle will kill any fox alive, but ruin the pelt with a very large exit hole. The only .22 centerfire that I know of that does not leave a very large exit hole is the .22 Hornet - and you really need to handload if you want a Hornet to shoot well.
I had a Savage in 17 like you mentioned. Mine wouldn't shoot very well. With most ammo it was a 2" rifle (at best) at 100 yards. It was even worse if there was any wind at all. However, most guys seem to like the rifle and cartridge.
If you don't handload you might have a tough time finding .223 ammo for a while. I have killed a bunch of foxes with a regular .22 long rifle rimfire, and it works very well at the ranges you mentioned