If your first rifle is likely to be your only rifle, spend the money, you get what you pay for, and regrets later are expensive. If you're likely to become addicted like the rest of us, well, go crazy! Buy what you like.
The 30-06 enjoys a crazy popularity south of the border, as it was their military round. Thus, you'll see lots of glowing articles on it, and various arguments about it's superiority over the 308. Militarily, the 308 is superior for one reason, it's ammunition is lighter to carry, and smaller when packing large volumes. To the sports shooter (unless you're crazy about packing ammo) that matters not. It's also one of the main reasons why current rounds carried by the military of most nations are much smaller than even the 308.
Another is the 308's ability to use shorter actions (shorter bolt throw) enabling very slightly lighter rifles with shorter OAL for a given barrel length.
In the field, the 165 grain is my preference for both cartridges, and at that bullet weight, there's bugger all difference between the two, particularly from the receiving end.
There are a lot of fancy and expensive rifles out there, and many will fill the bill. If budget is a concern (or it's your wife's concern

) take a look at Savage. If you can get over the bolt handle, or actually like it, they are accurate rifles out of the box.
Also CGN's EE is filled with rifles that would do the job for you. But you need to be fast, the best deals are gone within minutes of their posting.