Al80s make a great starter set, a great recreational set and a purdy darn good set for technical diving when planning for limited exposures.
They're relatively inexpensive, relatively managable on land or a rolling deck, and not as "floaty" as some folks believe.
I don't know that you need doubles, SS, but if you want to play around with some, then the Al80's will do you well. If you already have some extra cylinders, ptutting them together won't be such a huge investment. But remember... you will need a plate, a doubles wing, and two reg sets. It WILL add up!
Lynne,
I can't imagine any cave instructor recommending that you ship your twin 72s. You won't need them, for one, and they won't be enough for your cavern class. It's not unheard of to need two sets of Al80s to make it through the day. Maybe the GUE guys do it different but that's been my experience down there... two sets of doubles so that you don't have to go back for a fill.
The most popular exposure protection is a 3mm full with a 5/3 hooded vest. Often, a standard SS BP and a can light is all that is needed... the weight belt stays in the car. (Personally, I think that's cheating, but...)
I have dived dry and wet down there. With my drysuit and a 200 gm undie I use an Al plate and 8 pounds on my belt. I can't imagine that you would need anything like what you've mentioned above.
Oh... wet is the way to go, BTW.