Like the others who have commented here, I don't have any breed-specific recommendations, other than perhaps the pedigreed variety wouldn't be the best choice, since they are bred for purposes other than catching mice.
Where some people go wrong, and I have myself, is that it's quite possible to train a cat not to hunt, simply by our human reactions to having the cat bring us a dead animal. When we react with disgust, the cat is likely to pick up on that eventually, and consider hunting to be something s/he probably shouldn't do. Of course, most cats won't quit hunting because of that, since they don't generally care a lot about what we might think of something - they'll just quit presenting you with their kill.
I have a couple of very old cats, sisters who have been with me since they were born more than twenty-six years ago, and they have never hunted. One of them pounced on a bird outside once, held it for a few moments then watched it fly away. They would give a mouse a passing glance, as if acknowledging its existence, but never think that it had anything to do with them.
However, I have a three year-old who doesn't even play around with them. We moved back to our house after having lived away for a couple of years and, in the meantime, some mice had moved in. Ella would go after them with all seriousness. She didn't even look like she was enjoying it, but that it was a job that she took to diligently, spending hours waiting for it to come within reach.
She killed three of them the first week we were back. We didn't see anymore until she brought one in alive one day, and let it go in the house. I don't know what that was all about, but she acted like that mouse was her friend. It was standing on the bottom of the steps only six inches from Ella, and at first I thought she couldn't see it. Then she reached over and rubbed her head on the mouse as if to say, "This mouse is okay."
I don't think the mouse felt the same way about it because it didn't stick around long, and I've never seen it again since. But neither did it turn up dead anywhere.
When Ella brings me a mouse, a mole, a vole, a bird, or some other critter, she will wait by the door with it for as long as it takes, wanting to make sure that she gets credit for it. While I'd rather she didn't bring dead animals home with her, and I'd prefer she didn't kill birds at all, I don't want to confuse her and make her think that there's something wrong with being a cat, and doing the things that cats do, so I thank her for it, and praise her for being such a good kitty. Then I try not to let her see me dispose of the body.
I grew up on a farm where I was pretty much the only one in the family who viewed our cats as pets. To everyone else, their purpose was to keep the rodent population down in the barn. I think it's fair to say that most people want cats as pets today, and it must be awfully confusing for a cat when their gifts are rejected with horror and disgust.
Cats haven't been domesticated for as many generations as dogs have and, until very recently, even domesticated cats were desired for their hunting prowess. For most cats, I think hunting is an instinct that they'll gravitate to unless or until it is strongly discouraged, intentionally or otherwise. Being individuals, this isn't true of all of them, however.
