Update WebApp Design

See [this page](https://github.com/alyoshenka/neo/wiki/WebApp-Design) for a list of requirements.

Some potential starters (issues linked where possible, otherwise feel free to make them):
- Abstract styling into its own file(s)
- See `App` component. Currently `styles` object is defined in the component file, it would be much better if styles for individual components were defined in individual files
- Abstract `App` components into their own files
- Very similar to above issue, it would be nice if every `div` was its own component, for additional organization and functionality
- Redesign app structure to fit with React common file trees
- Add a `components/` folder
- #43
- #50
- #4
- #55
- #60