Ken,
I would recommend checking out the SCCi (
www.scci.org). Also, when you make it to TAG... you are required to climb Mt. Olympus and see the Pillar of Fire in Tumbling Rock Cave. It's the quintessential beginner cave, and will thoroughly kick your a**. All you need are pads, helmet, lights, water and food. Limrock Blowing Cave is another horizontal cave that is a pretty good beginner cave. Easy walking, and relatively short.
Both of these caves are managed by the SCCi, and you can find more information about them on their website.
Also, Sitton's Cave in Cloudland Canyon State Park (GA) is another good beginner cave.
Adam