I will be focusing on sibling relationships, and the first siblings we meet are the Bennet sisters.
In Chapter 1, we hear about the Bennet sisters from their parents. Mr Bennet calls them all silly with the possible exception of Lizzy, whom he describes as having "quickness" and who is obviously his favorite. Mrs Bennet seems to have 2 favorites: Jane and Lydia, whom their mother describes as handsome and good-humoured, respectively.
In Chapter 2, the other two sisters' names are revealed (Kitty & Mary), and some characteristics start to become apparent. Lizzy (who we learn is the second oldest) argues, unsuccessfully, with her mother about being introduced to Mr Bingley by Mrs Long; Kitty is fretful; and Mary "wished to say something very sensible, but knew not how." Kitty asks Lizzy about the next ball, which shows sisterly interaction, but Lydia boasts about being the tallest of the girls even though she is the youngest. Jane is the only one we don't read about in this chapter.
In Chapter 3, the narrator tells us that Bingley "had entertained hopes of being admitted to a sight of the young ladies, of whose beauty he had heard much," and later, at the Meryton Assembly, both Darcy & Bingley praise Jane's beauty. Bingley also calls Elizabeth very pretty, but Darcy refers to her as tolerable.
Mary, on the other hand, heard a reference to herself as "the most accomplished girl in the neighbourhood." Lydia & Kitty are happy because they danced every dance.
Already we seem to have enough information to tell them all apart: they may all be pretty, though Jane is evidently the prettiest. Lizzy is quick, Mary is accomplished in some fashion (and vain about it, perhaps), Lydia is forward, and Kitty coughs fretfully. :-)
[I actually remember being confused at this point during my first read (many years ago) about whether there was a sixth sister -- I didn't know that Kitty could be a nickname for Catherine.]