Feeding a rifle...
Don Simmel--I THINK what you're asking is, "what brand of .30-'06 ammo should I buy."
The answer is, you have to buy several brands of '06 ammo, take them to a range, and find out what works best in your rifle.
My experience is that plain-Jane Federal blue box ammo (NOT their pricey stuff!) works quite well as a go-to factory round, in many rifles. So that'd be my starting point. As said above, whitetails are not tough; you don't need a super-premium bullet to down them.
My experience is that in a .30 caliber, the 165 grain bullet is the right weight and size for the caliber, so I'd start testing with that were I you. If 165's don't give acceptable accuracy, in YOUR rifle, then I'd experiment with 150's. I would not go larger than 165's--and when I was much younger, I used 180 grainers in the '06 "for brush busting." Now I know that the pointy bullets are actually better for brush (The NRA experimented with this, years ago), and a .30-cal 180 is an awful lot of bullet to throw at a whitetail, anyhow.
Practice, practice, practice, with your rifle! Can't say this enough. Yes it costs $$$ to do--would you wish to lose a deer through poor marksmanship? This, BTW, is the very thing that got many of us into reloading.
Anyhow, good luck with the muleys, and of course we will need a post-action report, with pictures!