disclaimer-buckeyes cant uses centerfire rifles on deer
except with "kill" permits - So I don't know about shooting deer with an '06.
I have two 30-06's, both military flavor - 1917 eddystone enfield and a Garand
The Garand (with side mounted scope) shoots very well at 100 yards with 165 grain Nosler BTs, which many say is fine as white tail medicine. the Sierra 165 gr pro hunter BTHP also shoots well for me.
The Eddystone has just the peep sights, but at 100 yards from a rest, kneeling, prone, and standing I can put them into a deers vital zone.
more economically, the Rem 165 gr core lockt psps are available in bulk as components (the same with similar winchester bullets) and have been killing deer for longer than I've been on earth. You can buy a box of 500 and practice all year long for what some of the "premium" bullets cost for a box of 50 or 100. And after shooting that much, you'll be confident of you, your load, and your gun, which probably means a lot more than a better load with a "super" bullet that you haven't shot as much..........