Ok...going to do my best here...there is going to be lots of copy/paste here.
How do we kitten proof the apartment?
Biggest thing is make sure that there are no electrical cords, etc that it can chew on. Make sure there are no little places it can get stuck like behind the fridge, make sure all chemicals are locked up and check for poisonous house plants
What do we need to get before the kitten comes home with us?
litter pan with litter
any toys you want
anything you want for grooming
Something for it to sharpen its claws on
How old are they when we get them shots? How much do shots, spraying or neutring, or declawing cost?
First set of shots is usually around 4 to 6 weeks. You will have to call the vet to get the prices. Each vet is different. Average should be between $14 and $25. Some places charge more for shots if the animal isn't spayed/neutered. Same with neutring. Males are typicaly less than females, anestetic goes by weight of pet. I think a cat runs around $80 to $150 depending on the sex and the vet. You don't want to have the animal declawed. It is very traumatic, a lot of vets will not do it. In order to declaw a cat you actually cut off part of the toes. Think of having your own fingers amputated at the first joint. That is what is done to cat during a declaw. If you are worried about your furniture or whatever, get a cat tree. There are lots of ways to train a cat not to scratch the furniture
What kind of food do you give a kitten? Is there a *best* of anything you can recommend?
Don't give a kitten adult food
I personally recommend NutroMax because it is hypoallergenic and cats are really prone to corn allergies in food. Lots of scratching, fur coming out, running eyes (had a vet try and tell me that one of our cats was getting sick with a resp. virus and it was food allergy) etc. Flea allergies are the same way.
Litter-how often should you change it?
Depends on the cat and what you feed it.
You feed cheep food like you get at the grocery store you will have more poop and stinkier poop, feed something like Nutro, less poop and less stinky
Some cats don't care how icky their pan gets.
The vet that I worked for reccomended 1 cup of litter in the pan and change it every day where you could tell by the poop and urine output if there was something wrong.
You can get scoopable litter which you fish in every day, and there are pans that they make to go with it that will sift.
FUZZY MICE! Ask any cat. LOL!