[NJ/FL] Questions regarding custody and child support. Father was never around.

I plan on taking my son's father to court for child support and full custody. He left new jersey for Florida before my son turned one 4 years ago. Hes on child support for his 2 other kids. We never lived together and he never helped with my son. My son is now 5. I don't care if he gets visitation. I just wondering if anyone has been in a similar situation. Will I have to send my son to Florida? They have no relationship. My son doesn't remember him. What could the outcome look like? Any advice will help.