One thing I don't ever recommend is using JPA based libraries (Hibernate, EclipseLink, whatever). Run screaming away from that spec as fast as you possibly can. There are much better options for ORMs in Java that don't have the session management headache and endless string of gotchas that is JPA. Ebean is my current favorite.
As for the "framework", I haven't really found the need for one. Jersey/Jackson + Jetty + Ebean gets you 90% of the way there, just fill in whatever you want for logging and other minor support items. If you want something more pre-packaged with some of the service start/stop boilerplate built in there is dropwizard (https://github.com/codahale/dropwizard).