Basically, why did Newton write : "Plato is my friend — Aristotle is my friend — but my greatest friend is truth." ? What were the influences of these two on him ?
Newton (I assume the attribution is correct) was merely paraphrasing a well-known Latin phrase traditionally ascribed to Plato (though not found in any of Plato's authentic works). Roger Bacon quoted it as: Nam Plato dicit: "Amicus est Socrates, magister meus, sed magis est amica veritas", and Bacon's contemporary Thomas Aquinas cites it in a similar form.
It may be perhaps worth to mention that the quote is strongly reminiscent of a passage in Aristotle as well. In the Nicomachean Ethics (Bekker numbering 1096a), we read (transl. Roger Crisp):
ἀμφοῖν γὰρ ὄντοιν φίλοιν ὅσιον προτιμᾶν τὴν ἀλήθειαν.
For one might love both, but it is nevertheless a sacred duty to prefer the truth to one's friends.
Since a similar quote is ascribed to Plato, this may explain why Newton sees fit to reference both philosophers in his own version.
This he said when he was a student in Cambridge. The cornerstone of "science" education at that time was reading Aristotle. So he started reading Aristotle. But the new ideas were already "in the air". Accidentally Newton looked into Euclid... then Descartes... and started to think about "new science", that is real one, discarding Aristotle as he deserves. Source: Westfall, Never at rest (a standard scientific biography of Newton).