What do you think Edmund wanted to become and why?

Edmund wanted to become a prince, and he wanted to get back at his siblings for perceived wrongs. Edmind wants attention... to be singled out.

You mustn't think that even now Edmund was quite so bad that he actually wanted his brother and sisters to be turned into stone. He did want Turkish Delight and to be a Prince (and later a King) and to pay Peter out for calling him a beast. As for what the Witch would do with the others, he didn't want her to be particularly nice to them—certainly not to put them on the same level as himself; but he managed to believe, or to pretend he believed, that she wouldn't do anything very bad to them, “Because,” he said to himself, “all these people who say nasty things about her are her enemies and probably half of it isn't true.