I'd is a contraction of I would. Also, please note that this sentence is not correct ending in 'with.' Also the first answer, above, about the construction is incorrect. Correct: "You are the last boy I'd ever want to marry"

Imagine that she wants to get married, and that her choice is limited to ten boys she knows. She is talking to a boy named Ian. She likes Adam best, but Adam wants to marry someone else. Her second choice is Ben, but Ben is not available. As she goes down her mental list, Charlie, David, Ed, Frank, George, Henry, there are some that are not perfect, but she might marry them. As an insult she tells him ranks #10. She knows nine boys she would rather marry. He is the very worst of all. He is her _last_ choice. She probably means complete rejection--"I will never marry you." It is _stronger_ to say "I will never marry you because I know many other boys I would rather marry" than just to say "I will never marry you," because it implies she has many, many other choices.

I think it adds emphasis. You could say it without the ever, also. But no"with" on the end.

It means "I would." Also you would not say "marry with," just " marry."

It means "I don't want to get married with you"