Wire mouse cage
Probably the most common type of cage you’ll find; there are hundreds of different brands and types of cage you can buy from pet shops or online. There is ample ventilation, the mice love climbing on the wire walls, and it’s super easy to attach toys all over the place. The only down side I can think of is that some of these cages have only a tiny access door, which can make it difficult to catch a less friendly mouse. I also find them a bit of a chore to clean, especially as they get older and the powder-coating chips away.
Aquarium or terrarium
Aquariums can make excellent enclosures for your mice because they come in all sizes, are easy to fill with toys and easy to keep clean as no smells will sink into the glass. They are also good for people with cats, as they are too heavy to be knocked over, and with the right lid, will safely withstand a curious cat on top too. The main down side to an aquarium is that there is little ventilation and in the summer can literally cook your babies if you don’t take the right precautions. Using a mesh lid can allow some circulation, but make sure the mice can’t chew through it – you’d be amazed how high they can jump!
Plastic S.A.M/Habitrail type cage
These cages are really popular with the novice pet mouse keeper, though I wouldn’t want to have more than one to clean. They are great to look at, colourful and fun for your mouse, but all those tubes and compartments get really icky really fast. After a few weeks of scrubbing pee out of those tubes, you might change your mind about how cool they are.
Certainly the cheapest type of enclosure, many people forgo the expensive pet-shop-bought enclosures for a simple plastic tub. Basically, you buy a large tub from Kmart, cut out the top and cover with fine, metal mesh. Then, drill holes for the water bottle or hanging toys, and fill with whatever your heart desires!