Congrats!!! That is an amazing milestone.
As for cats, try to preview the kitty before you introduce your kid to the kitty to avoid a bad match due to the trauma of leaving a not good fit kitty behind. Most adoption places do know a bit about their animals so ask and be clear what you are looking for even to the point of explaining why. It does make a difference if they know the reasoning. An older cat (at least 2) would have well known preferences whereas a kitten, well you never know what personality they will end up with and you have to train them.
We just adopted two kitties and the four year old male will put up with anything it seems while our old cat (passed over in December) was very much not a fan of the boys. The three year old girl is still skittish, but lets them pet her. They came from a home with kids pretty much the same age as mine and a dog. They had to be surrendered when the boy developed cat allergies.
The other pet we have that is a huge hit with Bear (SPD, seeker with some aversions) is a rat that was rescued from a hoarder. He's not like normal rats, he'll just sit there and let you pet him like a puppy.
If you are looking into rabbits and want one that just wants to be held look at large breed females. The smaller you go the more active they are and males are more active than females. They can be litter box trained and do make good starter pets for kids to take care of on their own.
The pets to absolutely avoid for such kids are hamsters. They tend to be bitey, not particularly responsive to attention and very nocturnal. Rats adjust to the cycle of the household, hamsters as a general rule do not AND they tend to dislike being woken up to be held or played with.
