As @Khaled said, any of the leading distributions will have tomcat in their repositories, and will have 1-step text based commands to install and configure a running tomcat.
During installation from DVD/CD of the main Linux distributions, you are offered the option to select a base-server only package set, which will give you package management tools, openssh, some system services and the various shell and kernel packages - but no X-windows, desktop, or gui applications. Login is then via text on the console or remote secure shell only.
There are a few decisions/choices to make to select a distibution, if you have a green field...
Typically, the leading distributions are either running rpm/yum based package management (fedora, CentOS, suse) or dpkg/apt (ubuntu, debian) so if you are familiar with those tools, then pick one from the correct group.
Then to consider whether you are looking for a stable long term support version of Linux, or whether you want cutting edge features. For example fedora repositories contain version 7 of tomcat, whereas CentOS 6.2 is still on tomcat 6. As you mention reliable and stable as a requirement I would elect for LTS ubuntu, or CentOS 6.2 - but this is Linux we are talking about, its all reliable and stable ;-)
OpenJDK vs SUN HotSpot. Typically the Linux distros ship with OpenJDK configured, however you might have a need to run the Sun HotSpot JVM. I personally found it easier to swap JVM on ubuntu, however I am comparing to an ealier version of CentOS 5.7, but you should check if you are getting away from the basic packages. (If you don't know why you might want to swap out the JVM, the its almost certain this won't effect you, so ignore this and step on)