An RSS/Atom feed is usually fairly easy to build and can make for a decent read-only API. You can add your own namespace or use microformats for app-specific data.
It might also make sense in your app as the more common "subscribe" use - a user might subscribe to get recommendations for new artists that fit her taste etc.
That's a read API, then - it's a fixed URL that returns XML results... You might not need an API outside of this at all, unless you want to allow write operations.
Most of the plans I have are, indeed, based on GET commands. However, I do have ideas around post commands e.g. sending back an assessment of the quality of a recommendation.
It might also make sense in your app as the more common "subscribe" use - a user might subscribe to get recommendations for new artists that fit her taste etc.