If you plan on doing your homework at home you should build yourself a desktop. That way you can build in a decent gaming capability while you're at it. If you expect that you'll be doing work at the library, park, friend's house, or at school, then you'll probably want to get yourself a laptop.
Or you could build yourself a good desktop and buy a cheap Android tablet. Use the tablet when you're out and about, and for light work. For heavy duty work, lots of typing etc, you can switch to the desktop.