It all depends on your situation, your goals, and what you like and are able to care for.
You have your main dairy breeds:
Holsteins- BIG producers, big cows that eat a lot
Brown Swiss- Big like Holsteins, don't give as much milk though, good grazers
Jerseys- Smaller cows, high components but don't produce as much (though much more efficient as they don't eat as much as the big cows)
Guernseys and Aryshires- smaller than holsteins, somewhat higher components but not as high as jerseys, don't produce as much
Cows are generally gentle, friendly animals though it will all depend on how much the cow has been handled and how she is raised. As far as healthy, clean milk, that will depend on the health of the cow as well as the milking environment. If you get a sick cow or don't have a clean place to milk her and a proper way to handle and store the milk, then the milk won't be very good. But if the cow is healthy and you know how to properly handle the milk, it will be WAY better than store bought milk
But if none of those breeds work for you, then do your research. There are many other breeds that people use for backyard family cows. It works for some as it all depends on your situation and what you want/need.
There are Irish Jerseys, Dexters, Galloways, or even if you can find a cross breed (I know a few people who love their holstein/jersey crosses, Normande crosses, and even some angus crosses can give a decent amount of milk)
If there are farms near you, my suggestion would be to visit some (with permission from the farmers) and ask questions and see what they have.