My "walking" varmiter rifle is a .22 WMR with a VXII Rimfire, 2-7x28 Leupold on it. At least for shooting everthing from rats to racoons around the house and yard. I have lost (2) cats to coons this year.
The Minox ZA5 2-10x40 is fairly light, generous eye relief for snap shots and offers a good mag range for this role. No AO adjust but simple is nice for a walking rifle.
Walking rifle to me means not setting up to call in most situations. It should be in the 3-9, 4-12 range to still allow for fairly close in shots that may pop up. At the same time it should be light enough to carry for a mile or two in a manner that allows for a quick shot. I put an old Vari-X III 2.5-8 on the .222 Vixen that I plan on using for some yote hunting this winter. That whole package is under 7.5 lbs.
A 2.5-8x35 VX III Leupold or whatever in that range, will work just fine as a walk up varmit scope. I had one of those on my .45-70 for just the same sort of shots. I am becoming more convinced as I get older, that I do not need as much magnification as I used to think that I did.
I have a Swarovski 4-12x50 scope without AO, which I have used for 10 years now at the range and for also hunting in the mountains of Utah and Wyoming. At 12X on this scope the field clarity and contrast is no different than at 4X. There is no apparent parallax in this scope that I can find even at 12X on days with heavy mirage. The SFP reticle is always in the correct circle of confusion and is clearly on the mark.
I think AO is a great help when shooting off bags, if for no other reason than the fact it eliminates a question mark when things don't go so well. Once a load is developed and I have confidence in it and the rifle, I tend to set the AO to about 150 yards and just leave it there. A 200 yard setting might be even better. Not all my rifles are equipped with AO, but the majority of them are.