My lovely cat, Burt, is great - at bringing in live mice and leaving them for Ollie and me to catch and release!
(Not sure what type of mice they are, but they are a dark gold colour and really very pretty. The last place they want to be is in anyone's home - at least they always seem very keen to get back outside.)
However, if we can't catch them, we do resort to a very effective electronic rat catcher which has never failed. It gives them an electric shock so I guess it is as humane as you can hope for.)
Anyway, I think I would agree with the poster who recommended female cats - they are definitely more effective mousers. (On the other hand, male cats are more laid back.)
Maybe one of each is the best bet?