I agree that "At Filmore East" is the way to start. They're a jam band and this albulm catches them in their prime and at their best. "Eat a Peach" would my studio albulm of choice in terms of recognizable hits and overall musicality, but pretty much all of thier stuff was good, and still is for that matter. They are a much different band these days in terms of personnel, but they're still playing some pretty tight stuff.
You should be warned that it's possbile to really get hooked and end up with a big pile of Allman Brothers recordings. Hasn't happened to me (well, not exactly) but I do have most of the standard bases covered. When you get in trouble is the day you discover this massive website that is devoted to the sole topic of Allman Brothers concert bootleg CD's (many of which have been endorsed by the band over the years, and thus are considered to be 'legal'). It's kind of like the following of the Grateful Dead and Dylan. Some people just can't get enough of them!
Oh, and maybe one day you'll want to check out some of the studio releases by the Derek Trucks Band. I'd go this route way before getting into all of the AB bootleg stuff (some of which is terribly recorded, I'm told).