Cages

Your hedgehog's cage should be completely solid-sided. Hedgehogs are very clumsy and poor at climbing, but they don't seem to know that and often try to climb anyway. Generally a climbing attempt will result in an immediate fall which could cause broken bones. Narrow-spaced bars (like in Hamster cages) are dangerous because hedgehogs tend to get their legs stuck in them. Wide-spaced bars (like in rabbit or guinea pig cages) are even worse because hedgehogs can easily get their heads stuck in them, potentially causing a broken neck or even death. While some rabbit and guinea pig cages have a few inches of plastic before the wire, they still aren't fully safe as hedgies will still be able to make it up to the bars by propping themselves up on their igloo or wheel. Make sure that the bottom of your cage is solid too as hedgies will hurt their feet walking on the wire floors that are in rabbit hutches. You also want to avoid any cages with levels because due to their poor eyesight and lack of depth perception, hedgehogs will walk right off any ledge. Levels are only safe if both the upper level and ramp have borders around them. The best cages are plastic totes, glass aquariums, and C&C cages (with fairly high coroplast sides). 

Wheels

Bedding

Exercise wheels are a necessity for pet hedgehogs. Just like cages, they should be completely solid. Avoid all wheels with wire bars or mesh because legs can get stuck in bars and nails can get caught in mesh. You also want to steer clear of the sandpaper wheels that sugar gliders use as they will cause a hedgehog's feet to bleed. While some hedgehog owners use the plastic Silent Spinner wheel, we don't recommend them because there are open spaces between the two pieces that a hedgehog can get nails caught in. We use 8.5 inch Kaytee Comfort Wheels in our starter kits and they work fine for babies, but sometimes they can be a little noisy. If you do end up using that size Comfort Wheel, you will want to move up to a bigger size when you hedgehog's back touches the center pole. The next size Comfort Wheel is 12 inches, which is large enough for any adult hedgie. The flying saucer discs (we recommend the 12 inch size) are another safe option, but can be easily broken if your hedgehog is on the heavier side. Our favorite wheel is the Carolina Storm Wheel. They are completely silent, easy to clean, and are the perfect size for hedgies. You can only purchase them online because they are all hand-made. 

There's tons of options when it comes to hedgehog bedding. Wood shavings like Pine and Aspen are low-cost and work fine as long as the bag says "kiln-dried". Carefesh paper pulp bedding, paper crinkles, and Yesterday's News pellets are all safe options as well. You can use newspaper or shredded documents as long as there are no staples. If you are successful in litter-training your hedgie, you can just have fleece liners and puppy pads instead of bedding. Fleece is the best fabric to use for this purpose because it does not have frayed edges.
Avoid cedar bedding (it's toxic to all small animals and can cause death), cat litter (clumping or non-clumping, either way it's too dusty for a hedgie to inhale), and towels or other fabrics that have loops and frayed edges that nails can get caught in.