The "best all around caliber" is not necessarily the best gun for your BIL.
As posters have said, a 7mm Rem Mag is a very good all around cartridge, as is one of the .300 magnums. But for a gun that will be used primarily for whitetail, I'd go with a .270 Winchester.
The magnums are great, but a shooter pays the price in recoil, ammo cost, muzzle blast, gun weight, and barrel length. The are really unecessary for most whitetail hunting and really serve no advantage for most hunters, especially beginning ones.
A .270 will be easy to shoot, carry, and cheap to practice with. It will also be entirely suitable for western hunting if he gets the chance. I'd be quite happy hunting elk with a good bullet in a .270 for the rest of my life. Just tell him to switch to the Federal 150gr Nosler Partition or 140gr Nosler Accubond when he does so.