Should I use the complete install or the Tomcat package or do I need both? I installed my Ubutnu server with Apache, MySql, PHP (LAMP), Tomcat and SSH, and samba.
The complete install includes Tomcat and OpenOffice.org, so it sounds like you just need OO and the .war file, rather than an installation package.
Having said that, the installer sets up some important config for you, so if you've nothing else installed on your Tomcat server it might be better using an installer.