Ive had a couple of the pets mentioned above myself.
On birds - I just think the idea of keeping a winged creature in a cage is not good. I couldnt do it myself and if the kids get bored of the bird, itll never get out of the cage.
Hamster - I had a great little hamster when I was a kid, he certainly could give a nasty bite but the more theyre handled when theyre young the less likely they are to bite. However, he used to sleep for the winter in his little nest so wasnt much fun then!! About being stuck in the cage, he entertained himself in a wheel, a tunnel and various other gadgets in it, and slept a LOT.
Rabbits - have had a few of them, I dont like them being kept in a hutch, if I were to get another one Id prefer a larger area to keep it - however, brilliant pets, especially the females, very cuddly, and they do bond with you. The males can be more difficult, tend to want to mate with your feet a lot if unneutered and less into the cuddling.
Guinea pigs are great crack, same comments apply as rabbits, although the males seem less amorous! If youre getting two they need to be the same sex, guinea pigs of the opposite sex can and will fight to the death if the female rejects the males advances.
Rat sounds like a great idea, never owned one but did know a tame one, smart little guy and perfectly happy to be handled.
Most rodents will be fine for handling once you start them off very young.
A cat is probably the most hassle free of any pet, they really do look after themselves, besides putting out food and changing litter tray. They can be pretty cuddly as well.
As far as maintenance and injections etc... I cant remember any of my rodents ever needing much in the line of vet attention, however they need to be looked after in terms of gnawing blocks etc so the teeth and nails dont overgrow - I have a friend with a rabbit who constantly has it at the vet for teeth clipping and nail clipping, and some kind of on going eye infection - never had those issues myself - its important that kids learn how to look after a rodent correctly to keep them healthy.