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.
This case is a bit of an oddity - the work's been going on for years and has been presented in various forms at conferences, referred to in somewhat specialist publications and so on. Our press office got wind of it, I explained the situation, and it was generally felt that cos we were submitting a paper (which could take a couple of years to complete the review/publication process) and presenting it at the same time at the main linguistics conference in the US, it was reasonable to put out a press release. I was expecting it to go unnoticed, but was picked up by Radio New Zealand, the New Zealand Herald (front page), the Telegraph, the Glasgow Herald (page 5, above the fold), BBC Radio Scotland, Today, BBC Radio Wales and the World Service. I'm shattered, and generally want now to crawl under a stone.