For most of what you want to do with it, just watch for a sale on a decent laptop when the price drops into the $350 range. It won't be a screaming terror or magical gaming system, but it will be worlds faster than your current laptop. I picked up a Samsung with an AMD A6 processor, 4 GB of RAM, 500 GB drive, DVD burner and 15.6-inch screen for $350 just a few months ago. It blows away my old laptop, has a new battery and a 1-year warranty.
Finding one that doesn't come with Windows 8 will be a bigger challenge.