It was easier than I thought it would be to install Java and Tomcat. With a few apt-get commands, I had both Java and Tomcat up and running. The next step was to serve Tomcat through Apache. This was done by using the AJP Connector. Tomcat is running with AJP connector port 8009 and I can serve up JSPs and servlet content through Apache who is listening on port 80. Pretty slick :)
It was even easier to get a Rails app up and running on WEBrick on default port 3000.
Next steps will be to serve Rails content through Apache.