I've fostered loads of cats, some laid back, some aggressive some absolutely insane.
It has IMHO nothing to do with sex or colouring.
I'd say there is no ideal pet for a toddler, get a pet for you, I also second a more mature cat, kittens are like toddlers themselves, they get in to everything, get under the feet of everyone and if they trip up your toddler you could end up with a dead kitten and an injured child.
I don't foster any more since her Mistyness moved in but the branch of CP I fostered for doesn't have a shelter, all cats are fostered in people's homes or in specially designed pens in the garden. It's a bit of a pain having to visit someone's house to see a cat but you do get to see the cat in a home environment.
As thecatneuterer said rescues will try to match the cat to the right family eg I had some black kittens that went to a family with two children about 11 and 13 and I had a 19 year old cat go to live with a lady who was celebrating her 90th birthday.
The kittens would not be suitable for the older lady, the older cat would not have been suitable for the family.
My own cat would be fine in a family with older children, if you annoy her she bats you with a paw but with her claws retracted but she has a habit of wanting to sleep on any human who is around and while it's funny for me to have a cat settle between me and my kindle in bed I can move her if she tries to settle over my mouth.
Don't worry about litter training, mummy cats teach their kittens to do that so whatever age cat you get it will use a litter tray. Do ask what litter is being used though as some cats can be quite picky (At CP they try to use a variety so that the cat will use anything).
Welcome to the world of being a kitteh servant.