I'd be solidly in the buy a bolt and run .223 and 5.56 camp. Economical, easy to shoot, cheap, plenty of effective target range, great barrel life, versatile... on and on. Works great on deer with proper bullet inside 200 yards.
I love my 5.56 and 223 wylde bolt guns. They probably get shot most and are plenty effective on steel to 600 yards. 800 is ok too, but my 75 amax is getting awful small that far out for me. It does make you learn wind : ) though.
If you can get one of those lee hand loading presses, the one that doesn't use a bench, a set of lee dies and electronic scale you can be loading your own ammo in the space of a shoebox for probbaly about 100 bucks less components if you deal hunt.... Add in 90 bucks for 1000 primers, .25 cents per brass or less, .30 cents or less per bullet, and a lb of powder for 55 bucks. Bam you're golden and he's learning like a boss.
Ive loaded plenty of good ammo on that little hand press when i couldnt have a bench. Itll work just fine!
^ reloading opens up the world to you For stuff like this. Run a 308 win and H4985 powder and a light 308 bullet will give much reduced recoil but still plenty of oomph.... a light bullet and unique powder or similar will recoil like a .223 or lighter and be crazy economical. Hodgdon has reduced load data now too you can check out. ROOM TO GROW score is off the charts here. This would be my pick if 5.56 is off the table.
I imagine you could get the rifle set up as a pistol caliber. Fun, but man what a pain in The ass and it's a still a pistol cal... 22 creed or 22 250 are possible etc, but they are fucking harsh at muzzle, eat barrels etc.