Cheapest is definitely public transportation. Take Airtrain from your terminal to Jamaica Station and transfer to E subway to Penn Station ($7.25) (or take LIRR from Jamaica, more expensive but faster). Take NJ Transit train to Secaucus Junction ($4) and then local public transit to your destination. Most if not all NJ Transit trains from Penn Station stop at Secaucus Jct. and are frequent during afternoon/evening rush. Check the NJ Transit site.
Cheapest is definitely