(こんぽんてき) The – not exactly the secret roots – but the essential and underlying aspects of something – as opposed to the easily apparent bits on the surface.
(ほんらい) Originally or primarily. Emphasizes the historical roots.
(きほんてき) The basics (the emphasis is:minimum i.e. basic knowledge). Also means fundamentally (emphasizing the essential bits that various things or ideas have in common).   $$$
(きそ) The basics, not as in “for dummies,” but as in basic cable, basic health care needs, basic industries like iron, steel, and cars. Also has the nuance of the basis for a judgment. Example: “I am basing my opinion on xxx.”  基礎はxxxにある。
(きそ) The foundation (Just like English, ‘foundation’ can be used literally or figuratively)