StackMob has that prebuilt backend that you're talking about. It has the REST API and datastore/schema generation built already so that you can just start connecting and saving right away. By the way I do work at StackMob, so in the interest of full disclosure I ought to mention that! But I'm here as a fellow frontend developer.
I had to make a site for my fiancee and I's wedding, and I realized I could whip one up really quick and just stick it on StackMob - backend, hosting, everything.
An example saving/fetching data to/from StackMob via the StackMob JS SDK (built on Backbone.js):
var user = new StackMob.User({ username: 'ericktai', password: 'opensesame', ..});
user.create(); //this saves your user to the datastore on StackMob's servers in the background via AJAX
var users = new StackMob.Users(); //notice plural
users.fetch(); //this fetches all users
var user = new StackMob.User({ username: 'ericktai'}); //notice singular
user.fetch(); //this fetches my user from StackMob
Sounds like you're writing a JS web app, so you can also try our JS SDK that lets you connect to StackMob's backend - it's your datastore already built on servers. Here's a tutorial I wrote up to give you an idea of what that actually means programatically.
http://www.stackmob.com/devcenter/docs/JS-SDK-Tutorial
To make sure you don't run into any cross domain AJAX call issues, we host your html app also. This relieves you of having to worry about whether browsers support cross-origin headers or not.
Good luck to you developing! It's great that there are so many tools out there nowadays like aespinoza mentioned! Find the tool that works best for you :)