The picture shows a classic "trunk line" cross section. In the center are the blue (cold) and red (return) lines that carry the coolant (at the faucet end the blue line is connected to the red line, forming a loop). They are surrounded by beer lines (color coded so you can figure out which tap goes to which keg) and the whole works is surrounded by a neoprene insulating jacket.
You do need a pump. And a source of cold fluid. Other than a commercially obtained power pack (a 20' system would probably run around $1200 I think) some folks have had success combining a small chest freezer with salt water and a stainless steel submersible pump as a home made power pack.
The reason why the first three option on your list won't work is distance: 20 feet is far too long. The copper pipe thing is pretty much just for tower mounted faucets - really short applications, and the air-cooled PVC thing is for "through-the-wall" applications. 20 feet is trunk line time, no way around it.
If by sump pump you mean the type of thing installed in wet-region basements, that would be serious overkill on the power side. Low power (and low noise) are key, along with compatibility with the working fluid (things that work with glycol may not be happy with salt water, for instance).
You need a very small circulating pump - volume is not a concern here (there's remarkably little fluid in 20 feet of trunk line). There are small submersible pumps that can work well for a home-brewed system.
I know I've read of a few systems that were cobbled together, somewhere on the site. "trunk line" might be a good search term to find them...