How often do you want to hatch pure breed chickens? If you only want to do it once or twice a year, rather than all year round, you could keep them together when you're not breeding them. I don't have chickens yet, but my plan is to separate them into breeding flocks a few weeks before they're moved back to pasture in the spring (I'm thinking I will keep the coops together in my mulched garden over the winter) and just raise pure breed chicks in the spring. Maybe I'll let some fertile mutt eggs hatch later in the season when they're all ranging together, if I don't like the results, I can always eat them.
Hens can store sperm, I've heard it takes up to 30 days to insure paternity, so even if your flocks range together most of the year, if you separate your breeding flock from the rest of them for 30 days, you can make sure your hens haven't been mating with any other roosters recently enough to effect the eggs you want hatched.
Roosters can fight with each other, but if you make sure each of them has a good sized harem and enough space to feel comfortable, most breeds won't fight much, although a little sparring to establish dominance is normal, they'll usually figure things out and part ways before either is injured. This depends on the roosters though, if you get an aggressive breed, or you don't introduce them gradually so they can get used to each other, or you happen to have a particularly mean rooster, you still might have a problem.
Again, I don't have chickens yet, but I've been doing an extensive amount of reading on the subject, so this is all second hand info.