He will need to decide for himself.
Too may ways to go here for good advice unless we could set down for some time and get to know the man a bit.
Is he left or right handed?
He can choose:
An auto
A bolt action
A lever action
A pump action.
A single shot.
A muzzleloader.
In autos he can go with the Remington 742 or the Browning BAR or can go with a military style rifle in 6.5 Grendal, 6.8 SPC, 300 BO 458 SOCOM, 50 Beowulf, or 243, 260, 7.08, 308, 338 fed or 358 Win. Or use an M-1 Garand in 30-06
Bolt actions can be had from Savage, Thompson Center, Mossberg, Remington, Ruger, Winchester, CZ, TIKKA, SAKO, Howa, Weatherby, Browning, and then you can throw in military surplus arms that are still 100% serviceable and in some cases, as accurate as some modern arms. These include Mausers, Mosin/Nagants, Springfields, Enfields Swiss T Bolts, Carcanos, Jap 6.5 and 7.7s, and a few others, an they are available in calibers from 6.5MM to 8MM in metric calibers, and also in 30-06, 308, 303 British and 30-40 Krag.
Lever actions are available from Henry, Marlin, Winchester, Browning and a few importers of "cowboy guns" in 357 mag, 44 mag, 45 Colt, 30-30 30-06, 270, 260, 7-08, 308, and a few others too, and if you go to the used market it opens up a lot more with 30-40 Krag, 307 Win, 356 Win, 32 Special, and a lot of old black-powder shells from 38 to 50 caliber.
Pump.......the Remington 760 is the only one he can get new. Available in various chamberings from 243 to 35 Whelen in both 06 and 308 lengths.
Single shots are available in break actions and falling blocks from New England Arms, Rossi, Ruger Sharps, Winchester and Brownings. Chambered in a lot of shells from 243 to 500 Nitro.
Muzzleloaders can be had as modern inlines and of course, custom made rifles that have no limits on the way you want one made. There are also good "traditional sidelock rifles" made my Layman, and Traditions and Thompson Center.
That was a very fast and incomplete overview of the choices he has.
But no mater what he buys, it is only 2% as important as how well he learns to shoot it and how well he learns to hunt. That's 98% of the equation.