The way to deal with mice (or any pest, really) is to get rid of every possible source of food and water. This may sound obvious, but you'd be surprised by how many people don't get why they have a mouse problem when they are providing an excellent environment for the mice to thrive. It's the food. If the mice are getting in near a kitchen or pantry, make sure that all food is secured in thick plastic or metal containers that can't be chewed through. Clean up all crumbs off the counters and floors after every meal. Don't leave pet food bowls nearby -- exile them to a place far away from where the mice are getting in. Make sure that cabinets don't have boxes of food that can be chewed through. And clean up the damned mouse droppings; they'll eat those too if they must.
And the water! Human houses are very dry and are not conducive to pests unless you give them water. Don't leave standing water in sink basins or in bowls for pets. Fix any leaking plumbing or anything that gets condensation on it. Keep everything clean and dry. Don't leave drops of water all over the counters.
Plug up the holes. Mice will chew through most things, but anything that makes it harder for them will encourage them to go elsewhere. I've heard that steal wool is something they can't chew through, but I can't vouch for that through personal experience.
Cats are excellent rodent repellents if you're willing to own one (or three). It's not even necessary for them to actively hunt and kill the mice, their mere presence is a deterrent. Mice have a fantastic sense of smell, and the smell of cats (especially their urine) terrifies mice. Put the cat box near where the mice get in, but not the cat food (see above).
Traps and poison are fine as far as it goes, but they just treat the symptom, not the underlying problem. No amount of traps will cure a mouse infestation if they have what they need to maintain a sustainable population. Mice breed at a ridiculous pace, and you cannot stop them by killing them one at a time.
I would not let a mouse problem dissuade me from buying a house that was otherwise a very good deal, because mice are very easy to deal with once you understand why they're there and can take away their reason for being there. I would only worry about any damage they may have done and what it might take to fix it.