The two bonded quickly and it appears that he was very interested in Lily right from the beginning, though she only regarded him as a good friend.
The relationship between Dumbledore and Snape would be one of an unusually strong loyalty, so much so that Snape agreed to kill Dumbledore upon the latter's own request.
Severus was made a member of the Slug Club presumably because of his talent at potion-making and Horace Slughorn kept a picture of him as a student, clutching his copy of Advanced Potion-Making.
Despite this, Horace did not have many hopes for Severus's future, as his photograph was kept behind many others.
Harry also was influenced by Severus' Hogwarts house, and freely admitted that Albus could choose Slytherin if he wished. Severus, whose father was neglectful and possibly even violent, began to identify with his mother's family and created a secret nickname from his mother's maiden name, calling himself the "Half-Blood Prince".
His unhappy relationship with his father may have been the origin of his disdain for Muggles.