What are our options for carpeting the basement of a split-level house?
From a comfort and water protection perspective, I think you'll find it beneficial to install a sub floor.  I'd recommend one which allows for ventilation beneath it such as these 2x2 panels you can buy at Home Depot/Lowes

Dricore

This will give you a nice, warm "softer" surface to put your carpet pad on, and help protect from any condensation issues with the cold floor beneath by allowing it a place to form, and then with the proper ventilation openings cut into the subfloor (standard floor vent in the carpet to allow airflow) it'll dry out on its own.