A cage - indoor rabbit/ gunine pig one works well.
Bedding - either dust extracted woodshavings - not sawdust, not aspen wood as is poisonous to small animals. Cage liners which are made from 3 layers of fabric, need to have a litter trained hedgie really or you'll end up washing them everyday. Puppy training pads work quite well too. thats what i'm using at the moment. they are absorbant easy to clean up, just throw away and replace.
Food- to start with kitten bisciuts in a chicken flavour are best. look for ones high in protien and low in fat (less than 10%) moving on to adult bisciuts well around 7-8months old. I'm using a mix of Purina one, Purina proplan, IAMS and James Wellbeloved at the moment. Its good to have a mix of foods as no one food will provide everything a hedgie needs nutrition wise.
DO NOT FEED HEDGEHOG SPECIFIC FOOD SUCH AS VITAKRAFT - THIS PRODUCT IS NOT GOOD FOR YOUR PET AND HAS NO NUTRITIONAL VALUE WHATSOEVER. ONE OF THE MAIN INGREDIENTS IN THIS PRODUCT IS SHRIMP WHICH IS KNOWN TO CAUSE ALLERGIES IN HEDGIES.
They can however eat wet cat food. not fish flavoured. My little boy loves spikes relish hedgehog meat. Although it shouldn't be fed all the time its fine as a treat.
Treats - mealworms - most hedgies love them. Milo isn't interested but Allie is mad for them. However being a bit of a wimp i'll only give her dried ones and she seems to love them like this. This is only a treat as they are very high in fat.
A wheel - hedgie love running in a wheel - I use a silent spinner and they are great. I have the 12" one. Although this sounds big its the perfect size and gives your pet the room to run around.
Toys - cat balls work well - the small ones with the bell in. Toilet paper tubes - cut in half the lengthways so they don't get stuck!
Water - either a bottle or a dish. I started with a bottle for Allie and found she wasn't getting enough water, plus i'm yet to find one that doesn't leak! So i've gone to dishes now and they are quite happy. make sure its quite heavy though or they'll tip it over.
thermometre - just to check the temperature of the room your hedgehog will be kept in.
Scales - digital food scales - keeping track of your hedgehogs weight progression is a very good idea. When a hedgehog becomes ill sometimes the symptoms do not display themselves til its too late. Sudden weight loss can help identify a poorly hedgie and allow you to treat him/her more quickly.