Since Hedgehogs are nocturnal by nature, they very much enjoy a cozy dark place to curl up in and snooze. To find the right cave for your hedgehog you need to remember some key factors.
They are burrowing animals. This means they love to dig and burrow in their shavings to make the perfect hiding place. When digging around, hedgehogs will uproot anything that is lightweight. So buying a hut that is heavy keeps you from having to constantly flip the hut right-side up.
Hedgehogs sleep in a burrow so they like a dark and private hut. Look for a hut that the light cannot penetrate.
Since you most likely will be waking your hedgehog up for handling, you want a hut that is easily lifted.
Make sure that the hut has plenty of space for your hedgehog. don't buy a hut that is too tight for him/her.
Rock is the most preferred type of hut for a hedgehog, as it is heavy, dark and easy to scrub down. These types of huts can be found in the reptile department of a pet store, but are the greatest for hedgehogs.
Wooden hutches typically provide for more room than a rock hutch which is ideal, but they are harder to clean because of their porousness. If you cant find a good rock hut, a wooden one is a perfect alternate.
Plastic hutches are not the most ideal for hedgehogs, they typically overturn them when rooting around. They also are transparent and do not accurately replicate the a hedgehogs natural burrow. If you are on a budget, this would be a last resort and can be used but isn't suggested.