One thing to bear in mind as you begin to flesh out your concept is -- do not allow your desire to 'get something running' to trump your goals. Having had a cursory glimpse of your Kickstarter page -- I assume that your final system will be secure.
Having said that, HTTP is a great place to start. RESTful services, for all the jargon that wraps the concept, are nothing more than HTTP GETs, as are most services -- the URL itself contains the specifics and you can even write server code to turn a GET into an action on the server.
On the Galileo side, in my opinion -- the node.js library is great for this type of thing. I have a rudimentary HTTP server running at home, right now. It only serves a static page, but...by parsing the path sent by the browser, I can easily create a RESTful service.
The 'trick' is getting your Galileo exposed to the Internet in such a way that it works like a proper HTTP server.
I used a domain that I own to create a subdomain and configured my router to send the HTTP requests to the Galileo's private (WLAN) IP. I use the wired Ethernet for SSH to the Intel XDK development system.
This weekend, I will write the process up and you can get the gist of how to do the same from that -- it isn't particularly onerous, but -- there are a few things that must be setup properly to create this sandbox you are asking about.
My Galileo Gen 2 (It is 100% 'stock')