As far as REST goes: Meteor doesn't yet provide a supported API for serving HTTP from your application. This is intentional: in the not-too-distant future, your application server is likely to not be just a single process directly serving end users, but an arbitrarily parallelizable service behind a proxy tier. So we'll need to provide a supported API for responded to HTTP requests (for example, REST) that continues to work in such a setting.
If you really need to accept direct HTTP REST requests now, take a peek at how packages/accounts-oauth-helper/oauth_server.js
uses __meteor_bootstrap__.app
to hook into the Connect middleware framework. This will work for now, but we don't promise that Meteor will always be powered by Connect :)
Supporting REST endpoints is on Meteor's roadmap.
So is file uploads (that's what binary type refers to).