My suggestion: use a VPS
For a website hosted by a developer, I usually suggest a virtual private server. It's true that there are a number of hosting services that do have Ruby and RoR set up, for example: Engine Yard., and many others. However, these will have a commercial orientation and will be charging you for lots of things that a learning experience doesn't need.
Plus, what if you want to try Spring, or JRuby, or something else that's also non-LAMP? (Or, say you want LAMP+Ruby?) Now you might be even closer to enterprisey stuff with high prices for direct support, but on your VPS you can run whatever you want, you can have ssh access, you can run whatever versions you want, etc., etc..
Another thing to think about is Google App Engine. which is free in some cases. You can't run Active Record directly, as Bigtable is non-relational, but RoR is said to run.