I'm using Jboss for web applications without EJB's. Also relatively new to J2EE, and probably not using all the facilities of the appserver that might be useful.
To start with, your app should pretty much transfer without any changes. Possibly just a few tweaks to the deployment descriptors.
A couple of things in JBoss (beyond the servlet container) that I do use is setting up datasources, and access them in spring using JndiObjectFactoryBean; and using JBoss to run a scheduled task with a SAR (service archive).
You've also got JTA if you need distributed transactions, JMS if you want messaging, etc. etc. I don't currently use either of those.
If you need any further help with JBoss config on the bits I'm familiar with, I'll be happy to help.