I am 14 and I want to know if I am old enough to choose what parent I want to live with

No you cannot choose. Only a court can make that decision. However at 14 your opinion will be listened to. How much weight it is given will depend on where you live.

If you want to change custodial parents the non custodial parent will have to file for a modification of the custody order in Family Court.

Agree with Scott, when you are 18 and out of school, you can normally decide where you want to live, But you have to live with the parent who has legal custody of you. If you want to move to the other parent they will have to file in court for custody. While the court will listen to what you want ( and you will have to say why also) they will also listen to any other evidence why you should not if there are such issues