What caliber is recommended?
For a sidearm I’d want a revolver, 357 or 44 mag.
Most people get way too hung up on caliber. What's most important is that it is something you can use well under stress, have practiced with, and will have with you and ready when you need it. Most Alaskan guides would rather see someone show up with a well worn .30-06 than a shiny new rifle in a mega magnum caliber that obviously hasn't been practiced with much if at all. Hits are what count. Some reasonable choices:
44 magnum is the most popular. Then others like me use bears as a excuse to buy other large calibers such as the 454 Casull, .460, or my favorite, which is a Magnum Research in .500 S&W magnum, but its pretty damn heavy for more than a day hike, but the flame alone would burn his fur off and rendering him deaf.
Whatever you do, don't fall for revolver line. Five or six rounds and you're out of the fight and you'll never reload before that bear reaches you. The current trend in Alaska is a Glock 20, which fires 10 mm ammo. It has a magazine capacity of 15 rounds (unless you live in some socialist hellhole). There are two lines of thought on ammo. One is Buffalo Bore 220 gr and the other is Underwood Xtreme Penetrator 140 gr. For either round, it's best to replace the slide spring with a stiffer one due to the tremendous recoil of both rounds.