Both hamsters and gerbils have cheek pouches. Also, a lot of the information on this was inaccurate. For starters, hamsters only live 1-2 years (on average), not 2-3. Out of the nine hamsters I've owned, only one of them made it to three years. Second, hamsters, rats, and mice all burrow. Lastly, healthy adult guinea pigs have 41 teeth on average, not 20.
Hamster among these pets have cheek pouches. Other hamsters kept as pets are the various species of "dwarf hamster". Campbell's dwarf hamster (Phodopus campbelli) is the most common—they are also sometimes called "Russian dwarfs"; however, many hamsters are from Russia, so this ambiguous name does not distinguish them from other species appropriately.
Many breeders also show their hamsters, so breed towards producing a good, healthy, show hamster with a view to keeping one or two themselves, so quality and temperament are of vital importance when planning the breeding. The best-known species of hamster is the golden or Syrian hamster (Mesocricetus auratus), which is the type most commonly kept as pets. It is also sometimes called a "fancy" hamster.