Bear spray is the 1st line of defense. Very few full grown healthy bear bother people. When incidents happen the bears usually just want your food, not you. They are almost always very young bears (100-150 lbs) struggling to find food after being chased off by their mothers. A shot of spray to the face is usually far more effective than a gun.
But if I hunt, or choose to use a gun I deal with Black bear around here, and in 95% of the rest of the country. The average size killed by hunters every year is 185-200 lbs. There are some 400 lb bear killed every year and there have been about a dozen or so in the 500-550 lb range. I'd trust any rifle 7-08 and up here in GA. I usually hunt with a 308 or 30-06 with good 150-168 gr bullets. The bears I've killed and seen killed dropped like a rock with that combo. A 30-30 with 170 gr softpoints seems to work just as well. When camping and not specifically hunting usually a 10mm pistol loaded with 200 gr bullets @1300 fps. and/or a 30-30 with a 16" trapper barrel.
Inland grizzlies aren't that much bigger, nor harder to kill. Around 600lbs would be a big one. They tend to be more aggressive, so the odds of needing something would increase. I'd use the same guns/loads as black bear. Remember, these are only located in inland parts of Alaska and parts or Wyoming and Montana near Yellowstone. The chances of being bothered by one are extremely rare.
Coastal brown bear are the 1,000+ lb bear. But the emphasis on stopping these animals is way overdiscussed on the internet. Realistically there are only a handful of opportunites to hunt them each year and a hunt will cost $15,000 minimum, and could easily cost $30,000. Not many can realistically afford to hunt these. I'd still rely on my 30-06 loaded with 200/220 gr Nosler Partitions. This combo has proven to be as effective as anything else. The next real step up in perfromance are the magnums 375 and up.
The Alaska game and fish dept conducted tests several years ago and the 375 mag was their top pick as a large bear stopper. With a heavy loaded 30-06 as their 2nd choice. Everything in between just added recoil with no improvement in performance. Test data here.
http://www.fs.fed.us/pnw/pubs/gtr152