For any job that requires portability, the MBA 11" is just perfect. It weighs so little that it can be carried all day, more or less effortlessly, which - to my mind - would make it an excellent companion for a student. Actually, I wish that such a computer had been available when I was a student.
I have used it as a main computer, and loved it, because my work requires me to be exceedingly mobile; however, I tend to use it mainly for text based exercises, rather than viewing movies on the screen. So, to answer the question asked, can you use it as a main computer, the answer is 'yes' even if your eyesight is a lot less than perfect, as mine is.
The battery life in the 2013 models is also a bonus; it means that you shouldn't need the cables etc for an entire day.
However, the 13" is also a superb computer (I have one) - a screen which seems enormous after the 11", along with astounding battery life and is also an exceptionally portable computer. Either device will more than adequately meet your needs.
Moreover, whichever one you buy, I recommend - strongly - that you get as much RAM as you can afford, and then, invest in as large a hard disk as you can afford. This will future proof the computer to some extent.