That's your first question? Impressive
Start by developing your rails apps locally on your machine, learn
Rails first, and worry about deployment later. You can run script/
server from your rails app directory to start a local webserver on
localhost:3000. Once you've developed your app, you can think about
deployment, and that's a question for your hosting provider.
By the way, Ajax on Rails assumes you understand Rails basics already,
so you might want to pick up something else if you are really new to
Rails, and then use Ajax on Rails to get good at the Ajax part.