For example do I need 3 Bagon and 1 in each of it's evoloutionary chain or can I take 1 and fully evolve it and be done with that chain?
no need
You can take 1 Pokemon and evolve and still get the shiny charm(after having each Pokemon register in your national dex)
Source: I completed the National dex myself
You can evolve just one Bagon and it çounts as owning Bagoon,Shelgon and Salamance