if the tiger and monkey are going to joint a business, is it going to be a successful?

Well, it depends. Though both of you are kind, easygoing, but there are some differences in your values. So arguments may be hard to avoid. Anyway, if you can understand and tolerant each other more, things may be smooth in the future.
As for what business are good for you, it's up to you. Just think about what you are good at and what you want to do.