Web API: Decide on & implement file storage for uploads

[tadhg-ohiggins]

Currently the Web API is both storing uploaded files in the filesystem and putting their contents into the database, which is clearly wrong. I think the right approach is to use file storage, and abstract it to the point that it works locally and in production.

• Determine that there's no need to put file contents in the database.
• Determine the best file storage solution.
• Implement that solution.
• Write tests.
• Test it locally and in a production/production-like environment.