You're right...any bean from that hill will do it and the deer won't know the difference.
Gunwriter John Wooters said as much once in an article he wrote.
About 31 flavors of cartridge will be the 'best' deer rifle, depending on your taste, or something like that.
I picked a couple of Remingtons in the 7400 Carbine/.30-06 and a 700 in 7mm Rem.Mag.
Either will do for little deer or bigger animals, depending on where and how far the plan calls for and what bullet weight needs to be used.
Pick the one YOU like and have fun.