I like Rails Templater a lot. It is a command line tool to build a rails app. It asks you questions like "Would you like to use rspec? Pry instead of IRB?"
I have created a fork that adds authentication, twitter bootstrap and backbone.js and some other options. It is pretty easy to hack on if you have specific needs. I use it all the time and I would hate not having it.
It is of course a command line app and not usable via the browser but maybe it will still fit your needs. Or the codebase could be integrated into a client web application.
Update after comment
You may be able to bootstrap a sqlite database so the app can boot, then just using a form or a wizard to set up something that writes your database.yml and other configs, maybe by means of thor (makes appending/replacing text in files simple and is part of rails). You would need to somehow restart the rails app and migrate the database. You could keep the pg
or mysql2
gem (or both) in your Gemfile or again use thor to edit them from your wizard/form.
I also recommend using rails_config as Michael suggested. With the above solution.
If I had more time to think about the problem, I may come up with something cleaner but this is how I would do it if I had to right now.