If you want a basic, do all gun with manageable recoil, I would suggest either a 308 or 7-08. Lots of rounds available for these calibers and they will handle all of North America game. If you are getting a "lifetime" rifle buy a good Remington factory or even a semi custom built (there are several available here in classifieds for under $2K. I don't know your budget, but I like to spend at least as much on my optics as I do on my gun, as good optics are key to me. You did not mention if you hand load, but stay away from any new calibers, AI's or less popular rounds if you don't handload as you want to be able to get ammo easily.
If you want one rifle with one round for all your game (deer down), you will need to settle on a bullet in the 140-165 gr range. If you don't mind having different POI you can shoot both of these with different grain bullets, lighter for predators and heavies for big game.
Good luck and welcome to the forum.
