The easy answer is to go big or stay home, but that doesn't address your shooting or hunting experience. If you've hunted big game and have an idea what it takes to kill a big animal, that’s a start. If you're a gun guy with lots of rounds under your belt from guns that recoil when they go off, that helps too. But the first best step is to get a bunch of books: the trilogy of bear attack books by James Garry Shelton, and Stephen Herrero's Bear Attacks, their causes and avoidance. If you haven't spent much time around bears, these will give you a head start. Ignore most of the other bear attack books, they are mostly written for sensationalism. You can also get good information from the Alaska Dept of Game and Fish.
As to the guns themselves, a 12 ga shotgun is popular among many who carry defensive firearms for bears. They have the advantage of being able to use less lethal ammunition so that a bear might be scared away rather than killed. When lethal force is necessary, slugs are usually the best choice, and Brennekes are IMHO, the best choice of slugs. The shotgun is desirable in populated areas because shot and slugs don't penetrate to the extent that a rifle bullet does; this might also be considered a disadvantage in some circumstances. Another plus for the shotgun is that a good quality pump action is less expensive than a suitable centerfire rifle. Shotguns are often available with folding or collapsible stocks, which when combined with a short barrel, makes them friendlier if you are going to ride around in small planes or helicopters.
Now for the disadvantages. Shotgun ammo is heavy and bulky, limiting the amount you can reasonably carry. Shotgun shell brass corrodes in a short period of time when exposed to the elements on a daily basis, so its prudent to have enough that you can swap them out every 3 weeks to a month. Shotguns are suitable for only short range. Should someone be in trouble some distance from you, if you don't have a rifle, you're are little more than a spectator. Recoil from a shotgun can be heavy. Shotguns tend to be more fragile than rifles due to their thin barrels and magazine tubes.
IMHO, a .30/06 with factory ammo represents the minimum for bear defense. I got my son a .270, but I don't like him much. Kidding! With heavy handloads, the .270 is a giant killer. Whatever you choose, you must be competent with it, and it must be proven reliable as any mechanical device can be. Choose the gun and the cartridge that you are the most competent with and the most confident of. Practice lots. When you've practiced lots, practice lots more.
If you need to shoot, the action will probably be close, fast, and shocking. The target will be in motion. The tendency will be to fill the sight with bear and pull the trigger. Don't do it. The purpose of shooting is to stop the bear's forward progression, once you've don’t that you've got time to kill it with a follow up shot. The first choice is a CNS shot if that is an option. The brain is only the width of the snout, so don’t get confused by the width of the bear's head. The bad news is that the head might be in constant side to side motion, in which case a spine or shoulder shot is a better choice. But once again I'm getting ahead of myself. Choose you gun carefully, work with it, and ensure it will stand up to the rigors of wilderness travel. Waiting until you're hundreds of miles from help is not the time to discover you gun has a hiccup.
Weight is a killer on the land. After a few days of tough slogging and no sign of a bear, you'll be inclined to leave the gun in the tent. The heavier the gun, the bulkier the ammo, the more likely it will be left behind. Consider that when making your choice.