This is a big question, but I will try to answer it in brief to get you started.

Mr. Darcy wants (desires) a wife of some beauty who will stand up to him and be an intellectual equal. In other words, he wants/desires Elizabeth. However, he has been taught to be proud and to want (to feel he needs) a wife of a higher social class than Elizabeth. He is in a quite enviable position as to fortune, being a lord with a large estate and 10,000 pounds a year in income.

Mr. Bingley desires Jane, and she is also everything he perceives he needs in a wife. He has a large fortune based on his father's success in trade and can easily support a woman like Jane who has no dowry. His stumbling block is that Darcy persuades him against pursuing Jane: otherwise, there are no obstacles.

Mr. Collins wants/desires to please Lady Catherine, and for that he wants/needs a wife of sufficient social status to pass as a lady. He really could care less who he marries as long as Lady Catherine approves. He takes the first woman who will have him. He has an ample living as a clergyman and will inherit the Bennet estate, which will leave him quite financially comfortable. He can easily marry Charlotte even though she has no dowry.

Wickham is the hardest one to understand for certain. It appears he would want/desire to marry Elizabeth, but he wants/needs to marry for money, as he doesn't have any. It is hard to understand why he runs off with Lydia, who also has no money, except to imagine that he planned to love her and leave until he was paid off to marry her.