Laptops in the 500 dollar range are truly awful. It works like this:
1. Usable
2. Durable
3. Comfortable
Pick two
Since this is a laptop that you want to do school work on directly, which I assume involves a lot of typing, you definitely want to invest in something that has at least a 15.4 inch screen, preferably 17.1. If you don't, you will mess up your wrists horribly and regret not making that extra investment not only for the rest of your school life but the rest of your life period.
My suggestion is to find a way to free up a couple hundred extra bucks and buy one when they're all on sale after Christmas. If you can raise your budget from 500 to 800 you can get something that will last you 3-4 years without requiring service and most importantly will be comfortable to work with. HP Laptops such as the one that Pyree linked to you above are within your price range, but have downright horrible construction and in my experience are extremely uncomfortable due to a low quality plastic shell and inadequate cooling.
When you do shop, remember that your primary objective is to find something that "will make it much easier for me to do school work", not something that will give you repetitive strain injury or Carpel Tunnel Syndrome in exchange for small savings.
As far as brand names go, avoid HP like the plague. They have a bad name for a reason, they're the Ford of the PC industry and nothing will hurt you more than being unable to write an essay because your laptop screen is broken.
Asus is fairly new to the scene but their pricepoint is high and so is the quality of their products. I was personally underwhelmed by the EE-PC lineup but the more expensive Republic of Gamers laptops are very nice for their price (which is outside your budget but you might get lucky).
IBM and Lenovo laptops are anything but pretty but they are extremely rugged and as such are used very heavily in industry and commerce. Consider looking around for a used Thinkpad, you won't be disappointed.
Sony is starting to make a name for itself in the Laptop and Notebook market. They're better constructed than HP and while not particularly powerful, they are probably spot on for your needs. Keep an eye out for them going on sale after Christmas.
I've heard mediocre things about Toshiba but I've never really had to service any either, so I'll just throw that out there.
Hope this helped a bit