Well there you go, nothing better than trying an airgun or two or ..... in person!
If you rule out Deer - may or may not be legal in your location so please do check , TN just outlawed airguns for large game last year, boo - even a .177 does what you want.
A marauder ( Benjamin) in any cal. will take small game out to 50 yards , a .25 would take a deer/hog but shot placement is everything and again, check the laws.
You could get say a marauder .25 ( more than needed for most things) and a hand pump for under $600.00 there after it's just the low cost of pellets.
ANYTHING shooting solids ( .45 ammo, solid .25 slugs, ...) will need a solid 1,000 yard backdrop to be safe. Shooting standard diablo pellets though will give you the safety needed for firing up at squirrels & such.
Many many hogs and in some other countries MUCH larger animals have been taken humainly with well placed shots using .25 pellets.
Take your $600 AR and $200 tax stamp & paper work then hand load all your ammo and you still will not have the many advantages an airgun offers. Sometimes less is better.
DO make the drive to shoot others airguns, I'll bet your sold on the very first shot, then it's just a matter of desiding exactly what you truly need/want.
John