>> how much different are hamsters and gerbils than mice? I know their personalities are different, but what about care and stuff? <<
That is a huge question. Read some old threads in the different forums.
Spiny mice, fancy mice, white mice, agouti (wild) mice; dwarf hamsters, Syrian hamsters; gerbils.
I don't even know where to begin.
Mice dig more and are more jumpy than gerbils. A little. Depends on the individuals. Dwarfs are different from Syrians, way different. I don't know where to begin!
Care? Syrians have to live alone in a big habitat with a big wheel. They need to get out and play, explore, and forage for awhile. Dwarfs being smaller can do that in a big bin. Gerbils will dig more - and gnaw more! No plastic for them, but more wooden stuff. Mice love smaller wheels, tubes, and they gnaw, but are smaller than gerbils so they do not gnaw so much. Spiny mice are a whole different deal, but since you likely won't get any (or even find them) forget it. Well bred fancy mice from a breeder are rather tame.
NONE of these animals should bite when handled correctly, and all can be quite tame including dwarfs.
Oh, much less sweet fruits for dwarfs who are prone to diabetes.
Read some old threads and do some more research. Answering very general questions such as yours is difficult.