Our basement is also a "dungeon" - but after painting the walls pink, it is less awful.
We put in commercial grade carpeting about 20 years ago. It was a remnant, and it looks like the stuff that's used in hotel lobbies.
It has held up awesomely. Cat barf comes out of it easily.
It has no padding. I'd say the pile is about 1/4 to 3/8 inches high.
Much nicer to be on than bare concrete. Our floor was poured in sections and is uneven. Carpet is just laid down. It doesn't seem to curl up on the edges.