I agree that sheet vinyl is better for kitchens for preventative maintenance. There are alot more seams in the tile vs a sheet that will allow water to get underneath and pop them. The tiles are also going to shrink over the years and cause the seams to collect dust/dirt/grime and will look horrible.
As for the underlayment, I'm not sure about the peel and stick tiles...but for linoleum nails are not reccomended. 7/8" staples every 4" across the field and every 2" along the seams are the way to go.