The Weatherby Vanguard and Howa are built on the same action and all parts between the 2 are interchangeable. The Howa and Vanguard are both solid choices. They both however are the heaviest production rifles you will find and not my choice for an all around hunting gun for that reason. If the style of hunting does not involve lots of walking in steep terrain either would be a good choice.
The 308 is a good choice, hard to go wrong there.
Lots of good choices, Marlin XS-7, Savage, TC Venture, Remington ADL are other options to consider.