What family of animals are elephants in, in the sense that (analogously) humans are in the primate family. Also, where on the net can I access general info in this area, including a visual representation of the types and classifications of animals?

Lots of potential sources. Search under, say, Taxonomy of Life or Taxonomy of animals, or Classification of Animals.

I searched "elephant taxonomy"
ELEPHANTS - Scientific Classification (http://www.seaworld.org/animal-info/info-books/elephants/scientific-classification.htm)