An easy rule of thumb is the lower the number of the gauge, the thicker and better the stainless steel.
Therefore, 18 gauge is better than 20 gauge. Most undermount sinks are 18 gauge (Stone Masters Inc carries both options). 18 gauge is widely considered to be a quality thickness for use in a kitchen sink. Twenty gauge sinks are typically too thin to be recommended. While 16 gauge will likely outlast your kitchen!
The thickness difference between 18 and 16 overall is less than the thickness of a hair, so it comes down to a personal preference and budget decision.
Regardless of the gauge stainless steel is still susceptible to scratches and dents. Look for at least an 18/10 Chrome/Nickle content. The Chrome gives the sink its luster and nickle gives it strength, so if you want a sink that will stand the test of time 18/10 is the ideal ratio.
Sound deadening is another big issue. The best sound deadening is actually the pad, as they stop the sound from traveling. The spray just insulates the sound to muffle it. Many cost effective sinks will combine the pad and the spray to provide an ideal combination at a reasonable price.