There is no *single best* rifle or cartridge for hunting, no matter what the game animal. Depending on your hunting conditions, and style of hunting you do, will best drive the type of rifle you should use.
There are many quality brands rifles that will work well for you, no matter where you are or how you hunt. First and foremost you need to identify a caliber that you want to hunt with. Many calibers can be used successfully on medium to large size game animals. Some of these are the .30-30, .35 Remington, 270 Winchester, .30-06, .45-70, and many others. One caliber that stands out is the venerable .30-‘06. This cartridge will work well on any medium or big game animal on up Moose, Elk, Caribou, and Black Bear with appropriate hi quality ammunition or bullets.
A multipurpose big game rifle that suits most hunters no matter where they hunt, or the style of hunting they do is a quality Bolt Action Rifle. These rifles come in any chambering you might want.
Getting a bolt action rifle, chambered in .30-’06, with a good quality variable power scope of 3-9 power magnification will cover 99.5% of North American hunting needs. It would be an excellent choice for all but the big bears such as Alaskan Brown / Kodiak, or Grizzly Bears. It will even work on these bruins with proper bullet selection and bullet placement. However most hunters generally consider the ’06 to be too small of a cartridge for these big animals – I am one of those.
One **specific** recommendation for rifles would be a .30-‘06 chambered Remington 700 ADL with iron sights, mounted with a mid priced Leupold 3-9X scope mounted in quality quick detachable rings.
Good Luck with your choice.