Regarding the winchester 30/30.....light, handy, accurate (not kidding!) and you can find one for around $250 used....and ammo in any country gas station. And more potent on critters (that is what I carry a truck gun for) than a .22, SKS, etc.
I often use an NEF Handi-Rifle in .243 Win with cheap Bushnell Banner 3-9X shooting Barnes TSX 85gr or Sierra 85 HPBT. It groups about 1 1/2" at 100 yards.
Cost: $200 (used) for the rig, so if it's stolen, not a major loss.
I thought the AR-7 would make a nice truck gun too. It doesn't, it sucks.
In order:
1) 12ga. Pump
2) 10/22
3) Any carbine length centerfire rifle. Platform is merely personal preference. I prefer scoped accurate bolt actions that will reach out and touch a coyote. If you're gonna carry a centerfire might as well be able to hit something with it.
mostly I ride my four-wheeler around the farm, but now that it is cold I use my blazer(S-10) and I use either my 10/22 with archangel and red dot scope, or my mossberg 702 with rails and a small walmart scope.
10+1 .22 Mag take-down pump with shortened barrel and internaly skeletonized stock. Note: no disconnector and a .22LR next to a .22 Mag at upper left in pic...