If app design is the only thing you'd like to do, then I'd say spend all your time and focus developing UI/UX expertise for mobile. In many developing nations around the world, smart devices are giving people their first exposure to the Internet. The way they search, browse, buy, and otherwise behave online hasn't been profoundly shaped by desktop computing (and all the extra real estate that larger screens afford). All that to say, I've begun to think of UI/UX design for mobile as a distinct discipline. Many fine web designers find it very difficult to make the transition over to mobile: almost like fiction writers trying to write poetry. Starting with web and moving to mobile may actually handicap you. But if you start by learning to be economical and use limited mobile real estate to its best effect, then you'll probably be a better web designer (if you decide to grow into it later) for it.

Hope this helps,
Austin