I can strongly recommend Dropwizard for the plan. It is much less stuffy/enterprisy and you can easily split big apps into smaller services. It is some glue code on top of Jersey run in embedded mode Jetty (thus very little ops work needed).
Play Framework is also nice, but a bit too much opinionated! Meaning hard to make it do something in another way, which happens in real world big applications...
I've used Dropwizard but with my latest project I dropped it in favor of assembling libraries manually. There's nothing wrong with Dropwizard per se, it's biggest strength is that everything you need works out of the box, but it bundles some older versions of libraries (like jersey, jetty). I am now using latest Jersey, Jetty (embedded), Atmosphere, Ebean and RxJava with Kotlin. It wasn't that hard to setup everything manually and the benefit is that I can add anything I want. I work with Python and C# mostly and don't have that much experience with Java/JVM, but I really like this setup. I've also considered Play 2 with Java, but it didn't feel right to me and the documentation was out of date. Perhaps it's better with Scala, but I don't really want to learn an entire new language and ecosystem. Kotlin is similar to C# so for me it was a breeze to pick it up and I can transparently use any Java library with Kotlin by just importing it.
Jetty is up to date, but Jersey is old yes. But the new jersey is also a bit problematic, more stuffy and slow (from the benchmarks of others, I haven't done it myself). But the good thing is, there is a big and passionate contributor community around dropwizard (check their github/google groups) and this means if the new versions of libraries are worth updating, they get in pretty quickly.
