In my limited opinion, for school, the only concern should be weight, heat, warranty, and ample hd space. You are only taking notes on a powerpoint slide or using word, and internet surfing. The 13" laptop (whether it be mac or windows) in most cases will be cooler, lighter, and more convenient for class work. This would lead me to suggesting an ultrabook or a 13" dell/mac. I only lean against the ultrabooks because no CD-ROM, and while CD's are outdated, I have used mine a lot more in the last 2 years than I would've realized (I was considering buying a macbook air).
I like my 15" dell and it fits in my messenger bag, but sometimes I feel that it is cumbersome to hold and take notes, especially in a lecture hall (mostly b/c of the size and heat). I am not so worried about the battery since I will never be in lecture more than a few hours, and there are always plugs.
Since the laptop is meant to be portable for the first 2 years (class, home, library, etc) get something that is comfortable for you and maybe look into a monitor to convert it into more of a desktop. With most computers now you can quickly alt tab or change desktop screens to other open programs, so having a 15" vs 13" to have more than 1 thing open is kinda a moot point.
edit: Don't worry about the battery life. Most people plug their stuff into outlets in lecture/library/starbucks. If you get a portable power splitter you will be the hit of the class (can't tell you how many coffee's people have bought me when I whip out my splitter to share an outlet).