Hello, I am just like you and wanted a small Linux laptop for school so I went with a x201e which cost about $300. Let me warn you this laptop has a gma which means you won't be able to play many if any games on it. But there are a few that you can get to work on it for example I was able to get VN, and world of Warcraft on it! I was able to get it to run for about 6 hours when doing a paper in the car, but if you want to watch videos unplugged it will last about 2-3hours.
Here is a link to the laptop
http/www.amazon.com/ASUS-X201E-DH01-11-6-Inch-Laptop-Black/dp/B009F1I16K
(sorry if it isn't hyperlinked I was typing this on my iPad
)