I moved from Alaska last October and hunted caribou with everything from bow to rifle. Shot the caribou in my pic with a 7mm-08, one shot and down it went. I shot another with a .300 RUM, was out on a griz, caribou mixed bag hunt.. There is always a chance of coming across a bear just be carefull around your campsite and keep the meat and your food well downwind. Most guys myself included, used our trusty 30-06's most of the time. I carried 180 grain bullets for caribou and had a few 220 grain bullets for after the fact. Two things I learned that helped with keeping the blood off of me is always use latex gloves and do your quartering and skinning in your rain gear on.
Make sure you read the regs on meat salvage, AK fish and game dont play if you waste anything. Another tip is pick up some citric acid, mix it with water and spray the meat to prevent bacteria from forming and it will stop spoilage.
