Hard to go wrong with a 30-06. I'd happily hunt 90% of the game on the planet with one and I'd hunt anything in North America with it. There is some heavy game in Africa and Asia that I'd be hesitant to hunt with it and for some of the heavy game it wouldn't be legal but for North America it is a great cartridge. The wide variety of bullet weights make it one of the very best all around calibers. Recoil normally isn't bad. Ammo is readily available. Reloading components exist in any combination you can think of. All around it would be a good choice.

As to the type of gun, I don't think there is any company that doesn't chamber a rifle in 30-06. I've used and shot REM 700s for years and I like them. But I've also used Ruger, T/C, CZ, Savage, Win, WBY and a few others. It pretty much comes down to what you like. My suggestion is to go to a big gun store and handle as many different types of rifles as you can. Caliber isn't important just handle the different makes and models and see which fits you best. Things like stock design and safeties can and do make a difference. For instance, I absolutely hate the 3 position safety on Win rifles. When I throw it to my shoulder I can't find it easily with my thumb so for me Win is at or near the bottom of the list. Others love the 3 position safety and that is why they make different things for different people. When you handle a bunch of different types your likes and dislikes will become apparent.