In the $300 and bellow range you are going to be stuck with the slower AMD processors, and it will not last you through your college years.
If you can just get yourself up to the $400 range then we can find a decent i3 cpu that will be fast enough and will actually have enough build quality to last more then 1.5-2 years.
I would also highly suggest looking into OEM outlet stores. Lenovo, Dell, and others have outlet store where they resale returned laptops or laptops that arrived with a scratch for 10-30% cheaper with a full 1 year warranty still.