I'm going to take a loose interpretation of "most effective" As a general rule "most effective" goes soil>soiless(coco,etc)>passive hydro( hempy's,etc,>active hydro. Each of those categories can be broken down into different styles that may be better in that category. As an example,In active hydro, from least to "most effective" would go something like top drip>ebb&flow>dwc>nft>aero, although people will argue about that order.
Most cost effective would depend alot on the size of the grow, 1 or 2 plants a dwc would probably be more cost effective, but to do 30+ plants in a SOG, ebb and flow,nft or top drip would be more cost effective. I would have to say aero is the most expensive to get into, especially if you go true high pressure aero, rather than the low pressure aero/nft hybrid most run, which is still more expensive than the other systems.
Can't really say what I prefer as I'm just getting started.