My cats have proven quite effective over the years. However, i have used other methods as well.
I have used Ultrasonic boxes to good effect. They worked best in the garage plugged into the ceiling. You have to plug them in where they can "see" the entire room.
The big thing with mice in particular, is to find out where they are getting in.
Any crevice you see, stuff full of steel wool. Mice cannot chew thru it.
If you have no other animals, De-Con is a wonderful solution. It's is basically Warfarin, which is a blood thinner. Eventually the rodents die from internal bleeding. And there is supposed to be an ingredient in the poison that keeps the buggers from stinking as they decompose.
I have used glue traps to good effect. But you might want to BB gun on hand to dispatch the critters, as they panic and start to "scream". Also, if the mice are too small, a spring trap may only catch them by the tail, if at all. Again--BB gun to dispatch the little bastids.
Good luck, the bastids do breed quickly, so they must be dispatched in the same manner.