What kind of carpet padding for basements?

You don't put padding directly on a concrete floor. You have to frame out the floor, lay plywood sheets over the frame, probably want a vapor barrier as well. Then you can lay any pad and carpet you want. There are certain types of carpet that come with an attached foam padding that are designed to lay over concrete. If you think you want to just glue carpet directly to the concrete floor, check the mfg. warranty first. Most mfgs. will not honor their warranty unless they specifically state that it can be glued to concrete.