He sends mixed signals, what should I do?

Forget what Jack thinks about you... what do YOU think about HIM? Do you like him? Why? Sure, he's handsome and nice, and smart, and wealthy, but how do you feel about him? If he doesn't seem like someone that's worth spending time with, don't waste your energy. Live your own life for you, and if Jack fits into it, that's great. If not... meh.