Rails wasn't created for downloading apps and running them, It was created so that you can make new apps fast from the ground up. If you're coming from PHP that's a big difference, don't expect to take a project and customize. You are given the tools to create your own.
There are a couple that I could suggest you look at, but I don't think you'll learn all that much about Rails doing so.
ActiveAdmin: A DSL on top of your models which creates an admin system where you can login and edit all of the data ridiculously easily.
Refinery CMS: A popular CMS
http://guides.rubyonrails.org/, railscasts and peepcode are excellent resources for getting up to speed and productive.
Read the guides right through, they are spectacularly good.
The best way to learn is to start creating apps that you want to use, when you get stuck we can help you out.