I would not recommend a rabbit if you want something to pick up and hold. This is what my rabbit did to me when I tried to pick her up to move her.
I have a 2 month old, 4.5 year old and 6 year old. They don't pick up our bunny. First the rabbit doesn't want to be picked up so she just hops away when they try and second we made it a rule. I have been teaching Pepper the command "go home" so we don't have to catch her when she needs to go home. So far so good.
Pepper isn't afraid of the kids at all. She loves it when they scratch her head and they like to feed her treats and watch her binky and do zoomies.