Density--not thickness--is most important.

The Carpet and Rug Institute recommends a maximum thickness of 7/16-inch for residential carpet. If the carpet has a lower pile height, such as a berber or a commercial-like cut pile, the carpet padding should be even thinner--3/8-inch or less. But it should be firm and resilient. FHA minimums are 6-pound cushion under standard residential cut pile and 8-pound cushion under a thinner berber or low pile. Expect to pay about $2.50 per yard for quality cushion.