It will be much economical to use public transport. Public transport is available widely in Neelum valley (keran sharda, taobutt) and connecting big cities. However off-route places like Pir Chinasi, you have to hire taxi. (If you are a group of 3,4 people, then it will also cost effective).
Kutton is a in a side valley, you have to drop at Kundal Shahi from Bus. (Not sure about public transport b/w kundal shahi and kutton)