don't walk, sit
i grew up in western TN hunting squirrels.
well, actually, i watched them for several years before i hunted. but once i got guns (Rem 16 ga., then a .22), i used what i'd had learned by watching to kill some for stew. keyword: watch their behavior. even when you're not hunting, watch their behavior. Your son has more time for this than you do, probably.
here's the way i did it. ain't no better nor worse than any other technique, but it just worked for me. (and, given that civilization as we know it seems to be
deteriorating into anarchy, will probably use it again.)
my strategy was based in biology of the animal.
1) they eat nuts. look for nut trees where they will be finding food. walnut, pecan & hickory are their favorites in the east (unfortunately, also the favorites of furniture lovers, so there's far fewer of those trees now). they don't like acorns (oaks) as much; acorns are bitter (which would you prefer?), but will eat them if they must. in the west, the story is more complex, but since you're in Alabama, that'll do. oh, yeah, this means you'll need to learn to identify trees, which most suburban (let alone urban) dwellers have lost the ability to do.
2) the way to find a feeding tree: walk around your 'hunting ground'. look for fallen nuts that have been 'opened'. that means, the nut was harvested by said squirrel before it was really mature, but the outer 'green' husk of the nut was gnawed to expose the nut's 'meat' inside. you'll see their teeth marks on the nuts. look for fresh chips under the trees (tiny pieces of the husk) that have been removed from the husks. (of course, this is easier if you can devote time at least every few days to scouting your hunting ground. fresh marks means a given tree is ripe, and ready for hunting). look also for partially eaten nuts, since squirrels can be wasteful critters (like humans), not finishing the extraction of the food inside before going for another fresh nut. (sort of like partially finished plates of food i see all the time in Denny's or Red Lobster. it only happens in 'good times', though)
3) also identify watering holes. like any animal, squirrels need water. the nuts don't have that much. nut trees near streams or pools of water will be favorite trees, and due to competition for them, the biggest animals will be there.
4) best times of day to hunt: A) early morning (aren't YOU hungry when you wake up because some screaming jay won't shut the f' up?); B) late afternoon, after the heat of the day, the light of the day (when the hawks are flying on the updrafts) and before the night (when the owls are flying and can pick you off a limb because you bark).
5) walk very quietly to your nut grove at dawn or by late afternoon. pick a spot from which you can watch activity. sit quietly. watch the tree limbs. the key word is 'watch'. experienced squirrels produce exactly 0 dB of sound when they move, and they often move high in the canopy. (which makes your job with a HD shotgun even more challenging. consider adding a 26" barrel, mod choke if you can. .22 will work, but you'd better be able to shoot very well with those sights, or buy a scope.) As you are sitting and watching in the hopefully quiet woods, far off the highway, notice that you are enjoying life far, far more than if you were sitting in gridlocked traffic on I-X during your daily commute (an aging and stupid concept).
6) when you spot movement in the canopy: A) first make sure it's a squirrel, not a bird. (Hint: squirrels do not fly.) B) if squirrel, and if you're out of range, move ever so slowly and quietly to get as close as you can, but mind the angle. firing a shotgun straight up is not fun (read, it hurts).
7) if you are lucky enough to hit the squirrel, you may still have to find it. sometimes, they don't fall straight down. they get hung up in limbs. i've had to climb up 20' to get them. alternatively, throwing rocks or sticks up to where they're hung up can bring them down.
8) once you've got some (preferably two), field dress them (remove internal organs, which means carry a sharp preferably fixed blade knife; livers are worth keeping if you like the taste; can add a hearty taste to a stew. don't waste the brains either; they are rich and delicious. cook with eggs & chiles. warning: brains are high in cholesterol). once home, skin immediately and parboil and/or put in fridge.
9) i highly recommend squirrel stew of some kind. squirrels aren't cows, deer or elk. there's not a lot of meat there. there are many recipes for stew.
Here's one. If you like less hassle, just use garlic, onion, potato, tomato, green beans, corn & some mild greens along with some herbs & spices. I'd use basil, a tiny bit of oregano, salt, pepper.
10) to answer your other question about squirrel before deer, my suggestion is yes. deer are way more wary than squirrel, but contain probably 50X as much meat (not to mention more useful skin for making clothing should civilization as you've know it collapse). if you can't successfully kill squirrel, assuming there are some in the 'hood, it's unlikely you'll bag a deer either.
hope this helps. good luck.
NemA~