Best approach depends on your house design. How well-ventilated it is and such. Bait worked badly for us (at my orkplace) because the mice died in inaccessible places and smelt. Plainly pen didn't get that problem, but we did.
Neither poison nor traps will ever get them all, of course; making sure they can't get to any of your food is the most reliable way to make them lose interest.
I work on the principle that since they have access to a range of habitats we need to make ours as inhospitable as possible. Unfortunately, the age of the joinery is such that there's gaps and holes everywhere so getting these all mouse-proofed would probably cost more than moving to somewhere that's in a better state from this point of view. On the plus side, the number of poos I've found has been pretty small, which is suggestive we're not getting more than a few visitors. But if we catch more than four or five it'll probably be time to have a chat to the council to see if they have any wholesale slaughter solutions.