I think gerbils will be your best bet. My neighbors have three kids, the twin boys are both 4 and the girl is 7. They also have 2 gerbils, used to have 4 put they died of old age.
All three of the kids do great with the gerbils and vice versa. The girl can carry the gerbils around for a long time and they love it, both of them that is.
And you said you already had a cage, but you can get a ten or twenty gallon tank at a pet store for under $25. Gerbils are great pets, one of my friend has one, used to have 2 but again, one died of old age (he was almost 4), and she loves Lemon, the name of her gerbil. They are fun, energetic, friendly, and for people of all shapes, ages, and sizes.
Good luck with your search and it's good to know that you're doing a lot of research and not just buying an animal and finding out about it later.