Here are a few options, from a walkabout kind of guy:
A CZ 455 American in .22WMR. Lower-powered rounds for squirrel, CCI V-Max for larger critters like coons, porkys, and if necessary (and legal in Maine) 40 grain Maxi-Mags for Deer out to 75 yards, with well-placed neck shot.
Another option would be a 12 gauge shotgun, either pump or semi-auto. Shot for squirrels, buckshot for larger critters and close-range deer (under 40 yards) and slugs with a red-dot or holographic sight for deer.
When I'm on a walk-about, I usually take my CZ .22 Mag, but if hunting coyotes, I'll take my scoped, Tikka T3, .243 Win. I like to shoot, so if I don't see any game or varmints, I don't mind shooting a few shots with the .22 Mag at cans or other items I find on the property. I even have steel silhouettes that are left in the fields or along woods roads to test me. The .243 doesn't get shot as much, due to cost, noise and need to handload ammo.
Another option is a Ruger MK II or III with a Bushnell micro-red dot sight. I carry that when just walking about, and sometimes carry it along with the .243 Win, mostly for plinking. Squirrels are dead meat out to 30 yards with the MKII.
I've used a few Savage O/Us and don't like the weight and relatively poor iron sights. Mounting a scope makes them more like an anchor. I'm happier toting a semi-auto shotgun with various loads.
If I can't be with the rifle I love, I love the rifle I'm with!!