For non-technical business students who wants to pursue a start-up/entrepreneurial career, what are some pros and cons for starting their career in 1) project/product management, 2)Sales/Business development, 3)Marketing?

I'm not sure you are looking at this the right way round - you need to understand what your strengths and interests are before embarking on a path to gain experience in one of the areas you mention. That said, if you are intent on working at a start-up then the most useful experience would be in product management - i.e. a thorough understanding of the product development process. Product managers typically touch virtually every other area of the business - sales/marketing for customer feedback/insights, etc, business development for strategic direction, engineering as you work through what is possible and when, etc. As you gain experience as a product manager you may decide that biz dev, marketing or sales is more suited to your interests and preferences. Good product managers have a reasonable level of technical expertise, so focusing on this area will require you to build up your technical chops to compliment the business skills you already possess.