You'll get enough responses about getting a desktop over a laptop, so I'll just let other people do that for you.
However, if you consider portability to be important, then get a laptop. If you are just using your laptop in one place all the time, then you can consider a desktop. Right now, I consider portability to be important, so I have a laptop. For the games you want to play, you can definitely find a great laptop in your price range that can handle them.