I know that I'm probably going to get flak for this, however, I'm going to say just go ahead and buy a desktop (not a laptop!) and it will work fine. In this price range, you can sometimes (usually) get more for your money in my experience. Now, if you already have some of the parts and an OS of your choice, you can probably find a really solid build that will get you the performance you want in your budget. Just remember, if you plan on playing Minecraft at max settings, try and find a computer with a dedicated or discrete GPU and Minecraft will fly--the requirements aren't that heavy. I can get 60 FPS on normal settings on Intel HD Graphics and a Pentium, and pretty much unlimited FPS on anything higher than that (dedicated).