Gramps,
Nothing at all wrong with your first two suggestions. I'd opt for the Marlin as the action is stronger, and the added wieght cuts down the recoil. With 150 grain buller sighted in at 2 inches high at 100 yards, anything in the crosshairs out to 200 yards is gonna be called supper pretty quick.
I carried a Marlin 336 T for years, before ugrading to a used Bolt Action Savage in 30-06. I used to group 5 rounds in an inch and a half circle at 10 yards with a scoped Marlin.
I'm on my second Savage rifle (gave the first one back to my brother, bought a new one). I never would have tried a Savage had the price not been right, but glad I did. Even the package deal rifles are solid shooters. My old Savage 110B will still shoot 3/4 inch groups, my new 116 will shoot 1/2 groups. I've killed a LOT of game with the 30-06, killed an antelope with the 30-30 to prove it could be done.
If the young man doesn't reload, ANY name brand 30-06 will be made BETTER by shooting federal premium 165gr game king cartridges. This load has the best mix of flat shooting/knock down power out of the box you can buy for a standard caliber in the lower 48. It's no pussycat to shoot, but its a lot more power than the 30-30.
I've seen those Remington 760's for as little as $425.. and guess what? My dad has killed 4 elk, a couple deer and countless antelope with that old pump gun. Nothing at all wrong with that choice, exact same controls/ergonomics as an 870 shotgun.