Dear Alakendu,
If you are mostly interested in the relationship between Sanskrit and Greek, then may I also recommend an introduction to Indo-European philology? James Clackson's 'Indo-European Linguistics' is excellent and very readable; Ben Fortson's 'Indo-European Language and Culture', as the title suggests, also covers some of the cultural aspects you mention being interested in. Personally, when it comes to understanding language relationships, I also rather like Anthony Fox' 'Linguistic Reconstruction'. These are just a few of the books available on these subjects.
Given you say you may go back 'beginning with as early as Sir William Jones', just a brief note: William Jones, although a very famous participant in this debate, was far from the earliest. The first European missionaries who came to India and were able to learn Sanskrit realised right away that it must be related to Latin and Greek (many sources make that clear, the earliest western grammar of Sanskrit by Father Heinrich Roth SJ from the 1660s among them). William Jones was, however, the first to suggest (at least in writing) that the common source of those languages 'perhaps no longer exists' (his words in 1786); in other words, he suggested that, against earlier beliefs, the relationship between these languages was not that the western languages derive from Sanskrit, but that they all came from a common source and are thus sisters or cousins. That of course is the view that has been confirmed by philologists/linguists since then.
I hope the above is relevant to what you are looking into!
All the very best,
Antonia