There's a few things to consider when choosing the right cage for your hedgehog. You'll want a cage that is the appropriate size, can be sanitized and is safe for your hedgehog. Bars, platforms and ramps can cause injury and should be avoided. I've taken some popular cage options and broke them down into pros and cons.
I always recommend totes for cages. I find that the 105-106 qt totes from Walmart and Home Depot work the best for us. They are by far the safest cages for your hedgehog.
Midwest Guinea Pig Habitat
The midwest cages are another option if you want something other than a tote. These work great with fleece!
C&C cages can be made with grid storage cubes and coroplast. These are also great cages for people that prefer fleece bedding. Coroplast will need to be 8-10" tall.
Critter Nation Cage
A spacious cage option. All ramps need to be removed. Cage needs to be lined with coroplast to cover all bars. The lamp is usually secured to the frame of a shelf.
Wooden Cages & Hutches
I don't recommend these wooden cages, mostly because it takes a lot of effort to make them safe and sanitary.
While these cages are more appealing to look at, wood is near impossible to sanitize. The the urine will soak into the wood and harvest bacteria.
Plastic and Wire Cages
Hedgehogs are climbers and they can injure themselves on the bars. There have been cases of hedgehogs getting their heads stuck between bars, broken legs, bruising and injuries from falls. There are several different varieties of these cages available. Some also have platforms and ramps which are not suitable for a hedgehog. Hedgehogs have poor eyesight and aren't the most graceful creatures on earth. These cages can be altered by removing any ramps and platforms and by covering the bars with coroplast to prevent climbing.
Aquariums and terrariums
I do not recommend tanks of any kind. Tanks are designed to hold water/humidity and have poor ventilation, both of which will cause respiratory illness in hedgehogs. The cons definitely outweigh the pros on tanks.