Living in rural North Wales, mice are a common thing here. Things I have learnt:
1: It doesnt matter that my house is clean, tidy and isnt covered with waste food. If your neighbours are messy (or like around me, farmland) they will be around wether you like it or not.
2: If you can fit a pencil in a hole, a mouse can get in it. Wire wool/steel scouring pads has proven to be a good mouse proof hole filler, as have ceramic tiles cemented in place.
3: They are most active at dawn and dusk. Dont leave traps out all day as they will begin to smell of human, and mice will avoid them. put them out before going to bed and check them in the morning.
4: The 2 best things for baiting traps are bacon fat and chocolate spread.
5: Mice are half blind and run along walls and the bottom of units. Place traps along these run paths, probably indicated by mouse poo, mouse wee and grubby black marks.
6: Mouse poison is great, but a poisioned mouse will probably go back to its nest while dying. This is good as it can spead the poision to the whole nest (which could have 3 or 4 generations of mice in it - they can reach sexual maturity after 14 days and only take a week to gestate), but these nests are often between walls or under floors. Rotting mice dont smell nice.
7: Finding the nest and getting rid of the babies is better at controlling the numbers ahead of trapping the males foraging for food.
8: Find where they are nesting by following thier crawlway paths. Then do what I did and fill it with cement. No mice for 18 months so far.
9: Cats arent so great. They will play with them, letting them get away more than half the time. Little dogs are good - Jack russel or Scots terrier - they will find them and eat them most of the time.
10: The most reliable traps are the least humane. The old wire spring ones work best for me, followed by glue pads. The catch and release ones have on more than one occasion let a mouse escape. The little buggers then learnt to avoid them. Chasing them around with a hammer and a bucket was fun but pointless.