Peaches,
The snap traps are junk unless you tweak them. You need to bend the end of the tab (where you put the peanut butter) up just a little bit so that the trap has a hair trigger. Once you do that the trap works like a charm.
That's the most humane way to do it. Death is instant... Pellets cause them horrible internal bleeding and a slow death. Go with the snap traps, just make sure they have a metal tab and bend it up with a pair of pliers.
Poor little mice just want a warm place to stay.