I think the OP updated his post with more details after this comment was posted, look at the timeline.
OP, I think your $600 limit more or less limits you to a pump gun in 20 ga, or possible a semi-auto in 12ga.
The Mossberg® 500® Super Bantam Three-Barrel Combo Pump Shotgun in 20ga is on sale right now at Cabelas for $550, with 3 barrels.
If he can stretch dad's budget a little, the Savage bolt action rifled 20 gauge is $700 at Cabelas.
I own a Remington 1100 semi auto and I wouldn't recommend it to my worst enemy. They don't operate reliably unless you shot a heavy load. That nullifies any recoil advantage they have. New, they are expensive too. A 22" rifled barrel slug gun is much more suitable for close range deer hunting.




















































