I think your first step would be to go to your local electronics store and see what they have available in your price range. For what you have to spend you can afford something decent. Talk to an associate and tell them what you're looking to get out of your computer, and they can make some suggestons. You can also get a feel for what you're most comfortable using, and what looks good to you.
Both a desktop and a laptop will handle all of your email, documents, videos, social networking, music, etc. The main thing to consider is what you want to do with gaming. A laptop is more portable, but cannot distribute heat/power as a desktop would. Therefore a good gaming laptop is going to cost a lot more than a good gaming desktop. If you're really set on gaming, get the desktop. If you'd rather have something portable, get the laptop.
