Which action? Tough choice.
THe M98 is the original action for the rimless cartridge and all others owe it homage as all others have stolen something from it's parentage. I like the M98, especially for the 30-06. Even after 100+ years, it is still a very modern action. Also a very tough one to beat. If you want an American designed action, the Savage or the Remingtons get my nod. Either will build into a good long range rifle that is more accurate than most shooters and you don't need to spend a lot of money doing so. Stay with the basics, good barrel, good trigger, good bedding and good sights. Fancy wood, barrels and optics will drive the price of the package up quickly.
For what it is worth, my 30-06 was built by Winchester, the Model 1895. Perhaps not what you are looking for but a good action and hunting rifle nonetheless.