You can do better than a Rasberry Pi for that much money.
Just look for a Mini-ITX case and get a cheap AMD motherboard/CPU combination. Then you can customize it to your liking.
Or you could just buy something like this, it's already loaded with a HD, memory, and a CPU. It also has a media center remote, wi-fi, and bluetooth. http://www.newegg.com/Product/Product.aspx?Item=N82E16856173031