How is the ride back out?
Jim Wyatt gave me a great piece of advice before I dove Ginnie the first time. He said, "Make sure all the gas is out of your wing and suit, or the Devil will spit you in the river!" Jim was right!
To the OP-- if you want to stay in a single tank, I'd recommend just doing a cavern class. If you really get bit by the cave bug, go home and get into a set of doubles, and do an Intro to Tech, and come back and do Intro. It's really better to have redundancy in an overhead, plus, if you want to go on to Full Cave, you're going to have to have the doubles anyway.