If it's a laptop, you don't have to worry about building your own, you really can't without doing a lot of research and hunting around for parts. It's not like a regular desktop computer.
For that budget to get to 100 fps in minecraft you need to buy a used laptop, look for one with a 960m or higher video card, 960m, 970, 980 maybe the 8xx versions of those. The lower models will probably be running on lower settings to get those frame rates.