Ideally, deciding which type of design to pursue will be based on experience. Even if you create your own personal projects, try creating some print pieces (such as your own business card) and websites (create a mock-up of your online portfolio). See what you enjoy, and learn more about it!
Even if you have already decided on a print design route there is no reason why further down the line you can’t take what you have learnt, i.e Typography, Page Layout, Fonts etc and translate that understanding into the web.
Learning both print and web design will make you even more marketable. In today’s job market, listings often ask for a focus on one, but knowledge of both. As a company owner, being able to offer a client a full marketing package, with print materials and a website to match, will only help to grow a business and build an impressive portfolio.