In my humble opinion, Mandarin is definitely worth learning because it is the most spoken language in the world, and competency in Mandarin will give you an edge in your career and help you understand Chinese culture.
Regarding Cantonese, I think it's a waste if you don't make good use of the opportunities arising from your stay in HK to learn it, considering that there are so few written learning materials available. Moreover, there are many things in common between Mandarin and Cantonese. I suggest that you start off by using simple Cantonese sentences in your daily life, such as when shopping and ordering food in a restaurant. It will be fun.