My friends cat is having kittens and I might be getting one. She is an outside cat and they don't know who the father is. How do I know do I chose the right kittten?

Can Cancer or any other diesase be cured if it's a kitten?

Cancer is almost impossible to cure in an animals without expensive and intensve treatment, and there still is not a good prognosis.
However it is unlikely that a kitten will have cancer, as it is usually associated with older animals.

As for choosing a kitten:
The first thing is that the kittens should be at least 7 weeks old before they are taken from their mother.
Their eyes should be clear of ny discharge, and they should not have worms. Look for an extended belly or look at their anus to see if you can spot any worms around it.
They should be very active and playful, amost aggressive. (that's what kittens do)
Be prepared to be a responsible pet owner. At 2 months they should have their first set of shots, then a booster 6 months later; then another after 1 year. I buy my cat's vaccines at the "feed store" and administer them myself. It saves a lot of money & it's not hard to do. Some people just can't do it, but I pay $10 per vaccine. Aways ask for the vaccine with luekemia.
Please get your animal fixed also. There are way too many animals put to sleep because people aren't responsible about their pets. There are 4 cats hanging around my neighborhood right now, a mother and her 3 kittens. I'm fairly sure all 3 of the kittens are female. Think what is going to happen next year. I am trying to catch them & get them fixed as part of our city's "catch & release" program.
If you are prepared to be a responsible pet owner, why not get two kittens? They would keep each other company and are quite entertaining to watch.