Looking for Small Notebook

Hi!, I am looking for a very small, very cheap notebook/netbook that i can use for everyday use such as homework and browsing youtube and listening to music. It has to be portable enough to bring to high school on an everyday basis. I want to be able to do my homework at the school library since I am stuck there for hours waiting for my carpool.

Requirements:
-Small enough to fit in a backpack (that has books in it)
-Cost very cheap since I am a student in high school that cannot drive or work yet.
-Wireless internet (Of Course!)
-Enough RAM to run Word, Google Chrome, and Itunes at the same time. (Honestly 1 gb should be fine)
-I like to game so if possible be able to have some sort of integrated graphics such as intel hd 4000 (optional, since homework
main focus)
-Color choice would be nice (optional)
-Not ugly (You know what I mean) (Optional)
-Windows 7 or 8 is fine.
-Storage size should be reasonable for size (at least 200 gb)