[CentOS] Tomcat query from complete newbie

I'm a complete tomcat beginner -
(I installed it on my CentOS-6.3 server this morning.)
According to the web-interface on port 8080
tomcat is running fine.

Basically, I want to allow a Java program I have written
(which works well) to be run over the internet.
This is to test students understanding of Turing machines.
The student has to enter a short "program"
(consisting of 20-80 "quadruples").
My program will then test if the program does
what it is meant to do.

So the student enters his program (about 1k),
eg by pasting from a file - the program should then run,
and the student should see what it outputs.

I'm looking for advice on the best way to set this up.
As I understand it, tomcat can either be run "standalone"
or "behind apache".
I am running httpd on the server, so either method should be available.
It seems that the standalone option is simpler,
so I would probably prefer that.

Any and all suggestions gratefully received.