Wire cages work well, but make sure the squares are small enough so the hedgehog can't get out. An excellent container is a good size Tupperware bin. Drill lots of holes for ventilation, but not to big for your pet to escape. The bin works great and it can be disinfected. The bin should be deep enough so that a hedgehog's wheel will fit and be free spinning.
Bedding Never use pine or cedar.
Aromatic softwood is dangerous to their respiratory systems. You can use aspen shavings, or non-dusty clay litter. Choose the bedding carefully because the hedgehog will ingest some of the bedding. Aspen shavings are good because they are digestible. Warmth Hedgehogs must be kept warm.