I use 5 gallon plastic buckets. A local food store gives them away for free. (They had previously contained various food products.) They are of heavy plastic that mice can't chew through, (and I actually don't see signs of them trying). One 5 gallon bucket holds 25 pounds of feed or a little more. The lids press on securely. (The only drawback is that in cold weather, the lid can be a little hard to pull off.)
For smaller amounts, I also use plastic 2-gallon buckets with snap-on lids from the same place. They had previously contained olives or other bulk foods. They are not as thick and heavy as the 5-gallon buckets but the lids snap off more easily, and I have still never had a critter get into them. The lids to these come in various colors, so I use them to color-code different kinds of feed.