The three are all correct. The first sounds the least natural to me when using 'very much'. I would almost always use 'a lot', rather than 'very much'. "They want to win the role a lot" 'very much' is far more natural in the 2nd and 3rd sentences in my opinion.

The first one. Think of the sentence “I love you very much" when you are unsure. The second one can be said in certain contexts but the first one is definitely the most common.

I use number 1.