Stud the walls leaving the studs about a 1/2" to 1" away from the wall for an air space. Use regular 3 1/2" fiberglass batt insulation with the kraft paper faced vapor barrier on the inside/heated portion of the stud wall.
Any carpet and pad but use the best you can afford. Nylon carpet is best. They make a rubber type commercial pad but it is expensive so regular foam is ok. I don't think plastic on the floor will help much now (it should be under the concrete) but do you a moisture problem with the floor? If not, I wouldn't use plastic. If you did use a 6 mil plastic, it would have to be glued down since you also want to glue the pad down in an S shaped pattern so the pad doesn't bunch up under the carpet.
Other than that, I'll see if any of the flooring guys have anything to add.