Concrete floor over a good earth base may not need a lot of insulation, you just want to break the effect of the ground temperature (unless you're in a hot environment and would benefit from the free cooling and also have a way to control humidity to keep it in a safe zone). If the concrete has a good vapor barrier underneath then I wouldn't worry about moisture. If not, then I'd make sure to put something down. There is a rolled closed cell foam product made to go under floating hardwood flooring that serves as vapor barrier and cushion for the floor. Otherwise plastic sheet or foam board would work. In the old days we would just paint the floor. I remember doing several carpet jobs where we'd paint the floor, wait a few days, then put down padding and carpet. Always worked great.
Be warned, setting carpet tack strips down on concrete can be a major pain in the butt. We would always use construction adhesive as backup since you couldn't count on all the nails getting a bite. It was a miserable job sometimes.
If looks don't matter, I'd go with whatever is cheapest and easiest to install. Hard to beat a roll of padding and carpet when it comes to price.
Another option may be carpet squares. You put down contact adhesive on the concrete with a grooved trowel, give it some time to tack up, then lay the squares down. Carpet squares cost more but are super easy to work with. And if needed, you can peel up individual squares and replace them to deal with spills, stains, damage, etc.
