Scene 2 of Act 1 is actually a pretty enlightening and important scene, especially in terms of characterization. While we can interpret the scene to learn a little bit about Paris's character, we learn quite a lot about Lord Capulet's character.
One of the important things we learn about Capulet's character from this scene is that he genuinely cares about Juliet's well-being, wants, and needs. We learn this about Capulet through his response to Paris's request to marry Juliet. Capulet believes that Juliet is far too young right now to be married, as we see in his lines, "My child is yet a stranger in the world, / She hath not seen the change of fourteen years" (I.ii.8-9). Plus, she is his only child, and he most likely wants to enjoy her company as his child a bit longer, as he implies in the lines, "The earth hath swallowed all my hopes but she; / She is the hopeful lady of my earth" (14-15). Therefore, Capulet does not want to do Juliet any disservices by having her married too young. We also see just how important Juliet's own opinions, wants, and needs are to Capulet when he tells Paris that his own consent to the marriage is only part of what Paris will need to marry Juliet. Capulet believes that Juliet must also approve of the match; he does not want to marry her to anyone she does not like.
We learn less about Paris than we do about Capulet in this scene. But one thing we do learn for sure is that Paris is very obviously deeply in love with Juliet. This is evident from the fact that this is apparently not the first time that he has asked Capulet for Juliet's hand in marriage. We also learn that Paris is a very respectful gentleman, which we can glean from the fact that he refers to both Capulet and Montague as men "[o]f honourable reckoning" (4).
Therefore, while this scene seems to be of lesser importance, we can use it to interpret great deal about the characterization of both Capulet and Paris.