We're about to begin a web prototype project that has the following requirements:
1) Has very little data needs. Maybe 3-4 tables worth of data. Some very simple user management needed (login/logout/change password).
2) It needs support AJAX well and ideally works with a client javascript framework
3) Time is of the essence. This is a prototype project so let's not worry about scalability and long term benefits.
It depends what you and your developers are most familiar with. Any modern framework will support all the above, so if you want to develop quickly, use something you already understand.
If you are familiar with python at all, it's hard to go past Django in my opinion. I believe rails is also quick for prototyping if you know how to use it.
If you're looking at ruby. I would argue Rails. There are plenty of simple authorisation gems and generators (ie https://github.com/ryanb/cancan/) available. I've built a pretty simple prototype in the last week for a project here.
The one thing I will say for rails is there can be a few weeks of learning curve, but once you understand how it works you can prototype very quickly. Saying that, my first rails project I had a prototype using about 3-4 tables of connected data up in 1-2 weeks - now it is measured in days to hours!
My 2.cents, Node.js using express framework and mongoDB. I just recently worked on a project with a couple more requirements than you described. Had it up and running in less than an hour. Fits your javascript requirement quite nicely too. Nothing like having javascript on the front and back end.
I would take a look at meteor as well. It is made with the idea of getting a project off the ground fast. Its also built around real time data via web sockets or long polling depending on which browser is being used. It runs off node in a fiber which gets rid of the asynchronous nature of node (I'm not sure if that's a good thing, but the team felt it was better for the types of apps normally created with meteor I guess). The coolest part IMO is that you write the code once and it is run both on the server and client.
Other than meteor I'd also say take a look at laravel for PHP. Its got great documentation and a ROR like ORM.
I would suggest rails + backbone if you're in a hurry. Ryan Bates(RailsCasts) has 2 excellent and up to date casts on using the two together. The backbone-on-rails gem makes things easy. Really nice for a client in Backbone.js communicating with a rails backend through json.