you most definitely don't want to run your web application as root! never-ever!!
make it as secure as possible, - it will be hacked, it's just a matter of time (and popularity :) )
run tomcat as another user ('tomcat' or such) that can only read/write (if required) to it's own dir.
as for port redirection, I'd recommend using iptables, just as you showed.
alternatively you can do apache redirect as described hereas described here.
if you have a larger site and use hardware loadbalancers, you might map port 80 on the VIP to port 8080 on your web servers, in which case you don't have to do anything on the server side, and tbh, this is the best approach.