under a tight weave berber. I did that in my basement and the floor is softer than the upstairs (over a wood subfloor) and warm in the winter. You can save costs by going with a plush carpet. Do not get a cheap berber.
If you don't run the A/C, then do use a dehumidifier.
BTW - put the baseboards about 3/8 - 1/2 inch off the floor. The pad will go right up to the baseboards and the carpte will be tucked under. It looks good this way. Caution: beware of low spots in the floor (say by a drain). That's why I used 3/8".