Care
All small mammals need nice constant temperatures away from drafts or direct sunlight. Most are capable of keeping themselves warm as long as their location doesn't get too cold. For the sake of this page rabbits are getting labeled as large rodents, though that isn't exactly what they are.
Small Rodents
All rodents have perpetually growing teeth and need plenty of hard things to chew to keep them short, and to keep them from dismantling their cage furniture. There are plenty of commercially available wood products, that depending on species will work quite well. Expect to replace these frequently.
Most will pick a corner of their cage to use as a bathroom and another corner to use as a nest. Some hamsters can be taught to use a potty, but really they are rodents and you still need to clean the cage at least once a week.
All appreciate having an exercise wheel. Rodents are very active and in a small cage will quickly start acting very strange without a way to burn some calories.
Most rodents do best on pellet based diets that do not have seeds and such mixed in. Seeds can work as treats, but many rodents will pick out and eat only the seeds in mixed foods.
Large Rodents
The main difference here between small rodents is most larger rodents are not big exercise wheel fanatics. Chinchillas can sometimes be convinced to use a saucer shaped wheel, but animals like guinea pigs and rabbits don't do the wheel thing. This means they all need out of cage time to work off some energy.
Chinchillas and rabbits can be partially litter box trained, but it really only works for urine, they still will poop all over the cage. It is mostly a slightly more convenient way to clean the cage.
Most rodents do best on pellet based diets that do not have seeds and such mixed in. Seeds can work as treats, but many rodents will pick out and eat only the seeds in mixed foods. Chinchillas rabbits and guinea pigs should always have hay available. in nature their foods are no where near as calorie laden and they spend a great deal of time eating roughage. The standard hay is timothy, with alfalfa being good occasionally, but not as a base. Guinea Pigs can not form Vitamin C, so be sure any food pellet is high in vitamin C or be ready to supplement in their water.
Ferrets
Ferrets are the only carnivores in the small animal group. They have teeth and diet needs much like cats. Until ferret food formulas became commonly available most people fed them kitten food. They are also extremely playful and need plenty of human interaction.
Many will also need training to eliminate nipping and other obnoxious young behaviors.