If most of the projects you work on use Java or Python, I would start with those. In additional to a server side language you could also focus on a server side framework that will help you in ramping up. Like http://www.dropwizard.io for example.

I second dropwizard for building REST APIs.

If you know JavaScript, Node.js would probably be the quickest platform for you to start with. See https://news.ycombinator.com/item?id=9727658.

I know JS, however most of the projects I work on use Java or Python. I'm looking for a language that will give me a good understanding of the backend and will help me pick up other server side languages when I need to start on a new project.

In this case, my favorite back-end language is Scala, with the Play Framework. It has an excellent threading model, asynchronous processing, stateless model, a functional, immutable data programming style that fits well with multi-threading, great performance, and access to a vast array of Java libraries and tooling.

Python.