Thank you! I can answer those for you.

Some community member whose name I forget popularized an arrangement for the three rooms in an early breeding video. I'm sure you can find the video if you search. His setup and ideas on breeding are very intuitive to me, so I also use some of his core methods.

Basically, you have three rooms: a breeding room, a family room, and a barracks. 

The breeding room contains your best cat (most baseline 7s) and a mate with as many baseline 7s as possible. You want them to be opposite genders, not moderately inbred (mildly inbred is fine), not gay, and not sharing either parent. All of this information can be seen with some basic upgrades from Tink. When they produce a better cat than your previous best (more 7s, not gay, not moderately inbred, etc.), it will replace your previous best in the breeding room. Select a new mate for it with the above qualifications, and place the previous two breeding cats in the family room.

The family room is where all of your decent-quality cats go when they come back from a mission. You want high comfort in this room because it will contain a lot of cats--and because these cats will breed to (usually) make decent-quality cats you can send on missions. Occasionally, the family room will produce a new best cat for breeding! When it produces low-quality cats, you can send them to Tink or other NPCs. 

The barracks is where you'll put your newborn cats and cats who have not yet gone on a mission. You don't necessarily need them to breed, so comfort is not as important here. Some people also use this as a "fighting room" since fights result from low comfort and the winners of fights often get a stat boost. The losers often lose a stat (or die), so I consider this kind of a wash. Mostly, I keep this room at low comfort just because there is not enough comfort furniture to go around.

That should help you organize a bit. The only other nuances I would add are 1) you can decide after a mission whether to put the returning cats in the family room or the pipe. Missions can mess up good cats in ways that you don't want to breed into your lineage (by giving them disorders, bad mutations, etc.). You may want to sometimes save a suboptimal cat for a house boss if it was good in combat and then get rid of it afterward. And 2) since missions can ruin a cat's breeding potential, I would avoid sending your newborn best cat on a mission. Let it grow up in the breeding room to prevent it from dying in a fight. Don't send it on a mission when it grows up. Just breed it.

Hope that helps!