I was thinking .22, until you mentioned your son...If he is large enough to shoot the 20 gauge, I think you would have more success with the 20 gauge...

Early season squirrels can be tricky to pick up with a scoped sighted .22 and I think he might get frustrated trying to pick them up in the scope...That's why I would lean to the BPS, using high brass #6 shot...Get one with screw in chokes, I'd start with the modifed...Have fun!!!