Unfortunately in order to develop in Rails you will need to install it locally on your machine. There are a couple of options here. You can install all of the necessary files native to your machine, install a packaged development environment such as Ruby Stack from bitnami, or by using a virtual machine that contains everything you need. The best VM is Virtual Rails.
Heroku is awesome! It's incredibly easy to deploy your application to, and easy to work with. It handles both development and production applications very well. The basic (free) level can handle quite a bit, and you can scale heroku as your application grows. You don't need to deploy to Heroku right away, there are several web servers that you can develop with locally. Webrick is a built-in web server that comes with Rails. You can also look into using Mongrel or Unicorn.
You should also look into working with Git as your source control.