In particular, how does Jane Austen portray Mr. Collins and Mr. Wickham in Volumes 1 and 2 of Pride and Prejudice?
At first glance, Austen appears to portray the two men as opposites, but after completing Volume 2, the reader will see some similarities.
First, the two men are opposite in their "luck" with women. Mr. Collins cannot even get his own cousin to marry him which would enable her to lessen her family's financial burdens. In contrast, Wickham always seems to be followed by a crowd of admirers. Elizabeth, normally a very sensible girl, is fooled and flattered by him, and her sisters follow suit.
Secondly, Mr. Collins is attracted to sensible young ladies such as Elizabeth and ultimately Charlotte. Wickham is attracted to very young, impressionable girls (Darcy's sister and eventually Lydia).
The men's similarity is that they both really need to make good marriages. Mr. Collins needs a wife who will set a good example and who will help him in his relationship with the Lady Catherine de Bourgh, and Wickham needs to make a good match so that he can live "comfortably." He, in contrast to Mr. Collins, cannot seem to do what he needs to do instead of what he wants to do.
Austen uses the two characters in Volumes 1 and 2 to allow the reader to learn more about Elizabeth. Her opinion of these two men demonstrates her pride and her tendency to prejudge others, even if it's in a more flattering light than they deserve (as in Wickham's case). Wickham's character also allows Austen to show that Elizabeth is not a man-hater; she does sincerely like his company, and he one of the only male characters near the book's beginning that Elizabeth does not disdain.