What is the best custody advice for a parent who wants to move to another State with the children? Moving out of state and retaining custody legally can be a difficult maneuver for the custodial parent.
It is always best to work out an amicable arrangement with the other parent and to use mediation to work out child support issues, as well as, visitation schedules.
Definitely do have the modification documented officially and don't rely on a verbal agreement.
If the other parent refuses to agree to the move, legal proceedings will be necessary and you will want to find a qualified attorney to represent you.
First and foremost, you will need to put your needs aside and focus on "the best interest of the child or children" (I show a distinction here between child/children because, in this situation, what is best for one child may not be ideal for the siblings).
If you move out of State:

• Will the environment be more conducive to a well-adjusted upbringing for the children? (ex.
  rural vs urban inner-city)
• Are the schools better? (ex.
  ranked higher for scholastic achievement or better funded)
• Will the children have better care in their new environment? (ex.
  moving close to grandparents acting as daycare vs hired help)

These are the sort of questions you should be asking yourself and, in the end, putting forth before a judge to determine.
Make sure your claims are valid and convincing before you present them to a judge.
Your welfare and needs are also valid and should be expressed as well, just be sure to put your children's needs first when making a petition to the court, as that is their main focus in determining any custody arrangements.
Your needs might include such things as:

1. You have a good job (or offer) in the State in which you want to move.
   (this is a sign you have begun securing your basic needs and that you are prepared to move and you have thought it through.
   
2. Better standard of living.
   (ex.
   maybe you want to move to Texas where the cost of living is much lower than if you are currently residing in New York City, so you are better able to provide for your children.
   This is proof for the court that you are looking out for your children' future)
3. Your emotional -- mental -- physical support systems are in the State where you want to move.
   (ex.
   maybe you originally moved to your current State to accommodate your ex-partner and now that the separation has occurred you want to move back home because you feel isolated and alone and need the support of friends and family to properly raise your children)

Take some time and consider all the positive reasons you can list for moving the children.
Discuss these reasons with your attorney, then consider and prepare for the counter-arguments of the other parent.