I wouldn't get a hamster as they can be bad-tempered and have a very nasty bite. Also they're nocturnal so unless you want to keep rousing them from their sleep (and make them grumpy) they're not ideal for young children.
Rats, gerbils, mice and guinea pigs are all pretty good natured and easy to look after and they're all charming in their way. But someone has to be responsible for cleaning out their cages, feeding, handling, etc, and children can lose interest after a while, and, though relatively small, there is a cost involved - for cage, bedding, food, etc. I think most of these small animals only have a 2-3 year life span.
Elegran Your story about Winifred is absolutely lovely.