Integrate React.js

[perrycate]

I originally wanted to keep things minimal. React is not that. :P

Adding it anyway because:

1. When we eventually add the ability for multiple people to connect (Allow multiple users to connect at once. #8) and subsequent features that become possible from that, we'll be doing a lot more DOM manipulation. No need to reinvent the wheel, might as well use a framework.
2. I'm told the virtual DOM will make frontend testing easier (Add some tests #9).
3. I want to learn react.

[perrycate]

Also 4. As I add in other things (bootstrap, d3, whatever), they're more likely to play nicely with a major framework like react than with a lesser-known library like preact.