Restructure the HTTP handlers

[phpeter]

Inspired by this article.

I've added a context struct and a custom handler struct. The context only contains the DB now, but can also house user info, authentication, etc. The custom handler (via implementing the ServeHTTP function) allows us to check authentication and handle errors all in a single place.

Please let me know if you have any questions or if there's anything I need to change.

[sGerli]

@azertyfun , what do you think about this, is it compatible with your DB work?

[azertyfun]

It should be. I might have to manually merge a file or two, but otherwise it looks great.