Just also like to add that there is a framework called Spring Boot.
This is a very popular framework for building java based applications, and if you choose to build a web application with the framework it comes with an embedded version of tomcat,or jetty , or undertow within it.
Its very simple to run, and doesn't need an install, all it needs is a JRE and you just run the jar which gets built from your development environment.
This jar file has all of the dependencies needed.
It really is that simple.
Please have a look here:
I have used Spring Boot many times, but I havent had the opportunity to use it on the Pi just yet. Maybe you could let us know how you get on.