If you set up the server on a separate site as Drupal is concerned (subdomain pointing to a new site) then you will have to deal with accessing data from a different site which would probably be best done with Domain module. The all seems like a lot of overkill. Depending on the types of data you want to expose Services may do everything out of the box and it integrates with Drupal's permission and role system in addition to many modules exposing their data through it.
With services you can setup "endpoints" which have paths associated with them so you can do something like example.com/api/node ... etc. And you can alias build in resources so you can hide things like "node" and replace it with "content" or whatever makes sense in your situation.
Services is also able to version your RESTful API easy through Services tools (historical) so you can have api/1.0/custom, api/1.1/custom if you decide to provide custom resources. Versioning your API is a must if you want to ensure end-users are not interrupted by changes you may make. Services tools makes the process easy which you may end up having to do on your own if you build something from scratch. The services historical is being added to core services as well.