Just buy one for $500/600. You won't be able to do much gaming for $500 but it will get all your schoolwork done and last 3 years. Also, you might get laptop discounts being that you are a student. And warranty is important. I'd rather deal with one company for my laptop issues.
If you do want gaming. On a $600 laptop, you could game at Low settings for demanding games and High setting for LoL. Just make sure you get a laptop with dedicated graphics.