Hey! I've have quite a bit of experience with snakes. Generally, if the snake is in it's enclosure and can't get out, then it should be fine to have a cat around (though the cat might claim the heat pad/lamp
). Also, I wouldn't handle the snake with a cat in the same room, too much potential for the cat deciding to claw the snake, and in a panic the snake may bite you or the cat, or the cat can seriously mangle the snake
I'm a little hesitant to recommend a snake as a pet for a child. Though it's extremely rare to get sick from them (salmonella), people do get sick occasionally. Just wash your hands religiously before and after handling the snake, anything in the cage, or the snake's food, and as long as your don't kiss your snake, should be fine
With size, basically, the more you feed them, the more they grow. Genetics has some impact, but not a whole lot.
I don't recommend a king snake, especially for someone new to snakes or young people. They can be on the skittish side, can bite and once they latch on and start coiling, it's a pain to get em off. They can also be pretty tempermental eaters, and refuse to eat mice (they'll want lizards or other snakes which will be a challenge to come by for some people).
Like other's have suggested, corn snakes and ball pythons are awesome pets. Ball pythons might be better in this case since they're pretty slow moving. They crave heat so when you handle them, they'll tend to cling to your arm, rather than trying to get away from you. They don't get very long, but they do have considerable girth and weight once they become adult size, so might be something to consider (do you want to deal with a 10lb snake in 3 years?). Baby cornsnakes can have a but of an attitude, but their teeth are so puny it's more funny than anything else. They're also pretty fragile at that age. But larger cornsnakes are pretty laid back and calm, if you can find an adult cornsnake, it might be worth a shot. Cornsnakes I've rarely seen hit over 5-6 lbs, though they get longer (~4 ft).
Space is also a consideration. Ball pythons are more aboreal and like to climb so you'll need more vertical space in the tank. They also need more heat and humidity. Cornsnakes do climb on occasion but mostly stick to the ground, so you'll need more floor space.
Join a snake forum! Faunaclassfieds is a pretty good one. I think they have both python and cornsnake discussion groups. Just look around, tons of forums out there. It's also pretty fun checking out other people's snakes and chitchatting with em.
Good luck, and I hope you have fun with a new addiction. You can't ever have just one snake! Especially cornsnakes, so many different varieties and colors, you'll want one of each!