Refactor app to use new version of router

## Refactor app to use new version of router

### Acceptance Criteria
1. App works the same.
1. New version of router is used.

### Tasks
- Implement [react-router](https://github.com/rackt/react-router) 0.7.0
- Add nesting where appropriate

### Additional Notes
- None
Let's update these variable names to match the pattern we set later on. Append `Page`. (`ApiPage`, `ApiResourcePage`, `NotFoundPage`, etc.)