I'll try to answer them
The most common caliber was one of the .300 magnums ( usually the Win) when I started guiding in Alaska 35 years ago. then it was the .338 and now is probably the .375 ( either H&H or Ruger)

The smallest I recommend is the 30-06 but I have allowed hunters to use the .270 Win with 150 gr Nosler partitions and it works fine.
As for danger I would rate the big bears in between lions and buffalo. they are almost as quick as lions and the big ones as large a cape buffalo. Plus they are genuinely smart.
As for killing, I would also rate them in between lions and buffalo. They often react immediately to the shot, like lions, but can absorb a lot of poorly placed lead while traveling long distances ( if you are lucky and they are not charging)

Phil Shoemaker
Alaska Master Guide,
Alaska Hunter Ed Instructor
FAA Master pilot
www.grizzlyskinsofalaska.com

Anyone who claims the 30-06 is not effective has either not used one, or else is unwittingly commenting on their marksmanship.