I used the traditional spring-loaded traps, no bait (you want them to run over it, not slow down when they get to it, they’ll just steal the bait), just with the trigger against walls just outside of an opening where they would be running (like just at the edge of a refrigerator or near the hole they got through- if you can find it). I don’t think the spring-loaded traps are cruel (although their inventor, Hiram Maxim, also invented the machine gun, one sick puppy, huh!) because it’s so forceful, death has got to be nearly instantaneous.
Whatever way you choose, if you see a mouse, you probably have mice. Lay out a bunch of traps & replace them where they were successful until you stop catching mice.
A can of Great Stuff (sprayed foam insulation) is a good investment; scope out all the potential holes around sinks, cabinets, walls, basement perimeter, etc. and fill them in. I haven’t had mice since.