Optimal Range for 4x Scope?

Hello all, 

I joined so I could search and learn, which I have been doing the last few days. We have a 3/4 acre city lot that I have been tasked by the wife with protecting from squirrels and rabbits. I have decided on a HW30 .22 cal rifle due to it's size, velocity, and quiet operation. I know my wife will want to shoot it, as well as my 8yo son when he needs a break from shooting his Crosman 1322. The HW30/R7 is out of stock pretty much everywhere, but there is one I have my eye on that is bundled with a 4x scope. 

My question is will I been wanting more magnification then 4x if I am shooting less then 30 yards? Also, when I tree a squirrel they can be hard to find in the scope, so should I think about a peep sight as well? I am thinking a 2x7 or 3x9 Hawke or Bug Buster might help ensure I make clean head shots, but just wanted to get some ideas from those who know. 
 
If you are shooting 1/4 or 1/2 inch targets at thirty yards more magnification might be a good thing. The 4x scope on my 2240 was good for 1/2 - 3/4 inch groups at 50 yards for twenty years but, the eyes are getting pretty old, so recently installed a 3x12. I don't shoot much better if any but it is much easier on the eyes being able to see what I am shooting at. After 50 yards or so one inch targets get pretty darn small so the 2x7 or 3x9 would likely help and even at 30 yards it would be nice although not required unless you are shooting ants or flys. Had Hawke and Bugbuster scopes Hawke's are just better hard to say more.
 
I had the opportunity to use a 3x scope (actually a crosbow scope) and found it quite effective out to 35 yards on small targets. I could still hit my target at 40 yards, but making that his consistently in various lighting was a challenge. I would encourage you to check out the article here:

https://www.ctcustomairguns.com/hectors-airgun-blog/how-can-less-be-more


 
My .308 powder burner can hit clay pigeons at 300 yards with a 4x scope. The only reason you would need more magnification is for competition or if you are using the scope in place of binoculars/spotting scope. You will find high power scopes to be extremely limiting when trying to find a squirrel in the treetops, the small field of view is extremely limiting. I like fixed powers, because it is easy to learn to bracket targets for ranging with the reticle and your holdovers stay consistant.