What do you all want out of a small caged pet?
They all take work to become handleable and some will always be happier about being handled than others.
Mice and gerbils aren't great for small hands to handle, ditto the smaller types of hamster.
Larger hamsters IF you get one with a good temperament AND if you put in the work, can be better for handling... but still, typically don't love it.
Degus - nah.
Rats, yes, with the right habituation to handling, rats would be the best really.
They all have their distinctive pongs, mice being probably the worst followed closely by male rats.
Careful management of cage furniture and bedding can limit that, I have found rats to be considerably better smelling on Lignocel than on paper, for example.
Similarly, plastic shelves not wood, fleece hammocks that wash and dry easily, will hold less smell!
Boy rats do like to marinade in their own wee though, and boy mice dribble it everywhere.
Personally, if its a pet YOU want that a child will handle, I would go for rats.
Pick dumbos, they look adorable and have a nice group of three or four. Boys despite their pong, do tend to be much squishier than girls and much more inclined to snuggle, sleep on you, sit on shoulders etc.
Hamsters are very territorial and nocturnal, they are going to be active when a child is asleep and asleep when a kid is home from school/awake, which leads to them being fairly grumpy about hands reaching into cages.
As far as space goes, hamster and gerbils actually need about the same amount of space rats need, just no one ever gives them that!
If you want a pet that isn't really handled, I do like Degus, but they are like furry flubber, mini chinchillas on speed and if they get stuck in 'danger' mode the noise is VERY annoying!