"Get the best pad you can" is often the battle cry for carpet sales personnel and carpet shoppers alike. While this approach can extend the life of the pad a few years, sometimes the mid-range pad or maybe a pad with just a few extras like a moisture barrier or anti-microbial treatment can provide the quality and durability you need for a lower price. In the grand scheme of pad options there are essentially a few types to consider.
The most common is a rebond pad, normally comprised of foam remnants from the furniture industry that are formed into a solid layer normally between 3/8" think and 1/2" thick. The best ones are made with foam that has not been used (not "recrushed" foam), and usually have a density of 7 or 8 pounds (meaning one cubic foot weighs 7 or 8 pounds, respectively).
Another type of pad is a felt pad, comprised of strands of fiber, again from the textile industry. Felt pad does not normally feel as soft under foot, but is has a very durable construction, particularly for high traffic commercial applications. The cost is usually on par with the equivalent rebond pad options.
The top end of the pad spectrum is the solid foam rubber pad, which is made specifically for the flooring industry. The texture feels a little more consistent under foot and can offer superior longevity and comfort compared to rebond pads. Most solid pads come with moisture barriers that help prevent stains from seeping into the pad. The downside is the cost, which tends to be about twice that of rebond or felt pads.