The two most commonly available mechanical mouse traps -- the traditional "snapback" trap and the more expensive metal-lever-jaw traps -- are both effective if used properly. Wear gloves when handling the traps, since mice can detect human odors.
Use a lot of traps -- five to ten per mouse hole -- spaced at 2-foot intervals from the hole (mice only forage a short distance from their nests). Set them at right angles to walls, since mice scurry close to baseboards. By placing the traps perpendicular to the wall, the mouse will have open access to the bait area. Keep traps away from children and pets.
Set out the traps unarmed, with bait, for a few days to let the mice get used to eating food from them. For bait, use peanut butter mixed with rolled oats, raisins, or bits of whole-grain bread.
If you decide to use rodenticides and you have pets and/or small children, purchase a tamper-proof bait station.
Wear gloves when disposing of dead rodents.