For a well-funded start-up, there’s no web application hosting better than Engine Yard. I’ve used them and the level of support is better than I’ve experienced from any other hosting provider. With Engine Yard you get a team of sysadmins and application programming gurus who are leaders in the Rails community. You’ll pay for it (close to a thousand dollars per month for a staging server and redundant production servers) but it’s a better bargain than any other alternative if you’re rolling out a web app for the world to use.
If you’re not well-funded or ready to go live to the world with your web application, there are a dozen or more web hosting providers that specialize in hosting Rails web apps and will charge you less than $30/month for a virtual server. I’ve used MediaTemple and DreamHost. You get what you pay for and that often includes configuration headaches when you’d rather be coding.
You might prefer a newer approach, from Morph Exchange. They reduce the configuration overhead for deploying a Rails app.
There’s another alternative: Heroku. See the discussion here. James, Adam, and Orion have this crazy idea that you should be able to develop a Rails app and host it with zero configuration. And then use your web browser to edit the code! You sign up for an account and that’s it. Not only can you upload an existing web app and see it run immediately, but you can create a Rails app, or upload and edit an existing app, right in the Firefox web browser. This is an amazing alternative to the conventional model of developing an app locally and deploying it to a remote hosting platform.
The Heroku approach makes a lot of sense when you’re building an app to learn Rails. Or when you are in the early stages of development and need a way to show your collaborators (or potential customers) what you’re working on. Or if you are running any sort of web app that has no revenue stream to support it.