When choosing a Linux distribution available in Rackspace to host a Java application running on Tomcat (or JBoss) and accessing a MySQL database, what do you take into account?
For me it seems more a matter of taste; I wonder if a specific distribution has any advantage over others when hosting a Java application stack.
No Linux distribution has any distinct technical advantage for running a Java application stack.
The two main issues are going to be your familiarity with the distribution as well as what the vendor officially supports. If you want official support for your Java application server and the vendor only officially support specific distributions, you want to choose from their list.
Whatever you (as the operations guy) is more comfortable with. JSP will run anywhere. If you're going to run Ubuntu, use the latest LTS version. I'm sure other distros have something similar to an LTS version, use that with them as well.
I currently work at a company that deploys its main product onto Linux or Unix environments in JBoss, although we prefer an Oracle backend (or Postgres if you don't want to spend money). I'd wager it really doesn't matter, although you should probably use the server VM. You'll sacrifice a bit of start-up time on the virtual machine, but it's much better for applications that'll just be on constantly or need a bit more speed.
When it comes to what you should run it on, go with what you're most familiar with. You're deploying onto Rackspace, so you probably don't have tight technical requirements. If you did, I'd suggest one of the BSDs or similar so you don't have to deal with all that silly window manager stuff that those pesky Linux distributions come with.
JBoss is now a part of Red Hat, so you might find they encourage that in some places. On the other hand, if you're messing around with Seam and JSF like us, you'll probably find that what you deploy it on makes pretty much no difference anyway; most of your efforts will be spent configuring Tomcat/JBoss/whatever to work with what you've got. They've all got their little... quirks.
As with most questions of this type, it is a bit of a matter of taste.
That said, I prefer debian and derivatives because of their ease of upgradability. RH may be up to doing this now, but when I started debian was the only OS where I could install v1 and upgrade to v2 'live' - that is, without having to boot to an install CD and re-run the installer and such. Debian (and derivatives, like Ubuntu) still have this feature, which is why I tend to stick with them - I have a machine image that in 15 years has yet to require a full reinstall; I just keep it current with 'apt-get update; apt-get upgrade'.
