nginx mime types and gzip
Should I also include application/json?
Why not? The default
mime.types file from nginx only contains MIME types for more or less common file extensions. And it certainly isn't very common to have
json static files.
Also, what types should be gzipped?
You may include MIME types for all well compressible content that you have on your site. But for static files it will be better to use gzip static module.