For under $300, refurbished is definitely the way to go.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834299599
Is a laptop with an ssd, which helps enormously with boot time and opening up applications. But it is only 128 gb. If all you put on your laptop is microsoft office and only store your notes and projects on it, then 128gb is enough.
I'm a student as well, and I know that I like to store music and have a few pictures and games on my laptop.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834299597
Is almost the same laptop as the other one, but it has a 500gb hard drive, which is more than enough for a student.
I have a computer similiar to that, except with a 3rd gen i5 instead of a 2nd gen i3. I like having the extra storage, but there are several times that I'm waiting for my computer to turn on (or log on) and open up microsoft office while the teacher is talking and I can't take notes. SSD would greatly help this.
Regardless of your decision on SSD or HDD, these laptops are 14" and are very portable (although maybe not as thin as some computers)
One potential problem with any computer under $300 is the amount of ram. These only have 4gb ram. 4gb ram is plenty for just taking notes or having a few tabs open on your browser, but working on projects is different.
When I work on research projects/essays, I know that I use more than 4gb ram when I have several powerpoints and word docs up with 15 tabs open in a browser. (Usually takes ~ 6 gb ram)