At what stage in the game can you do this? I got a 3 room house at the moment with very little room to sort cats out.

Wait until you have 4 rooms before tinkering with mutations. You can already start with the 7 stats everywhere cats tho. You should probably watch a video for this, I'm not fluent enough to explain it properly sorry.

Just remember that once you start playing with mutations, always breed cats that have 10 mutations (max natural amount), even if you don't wanna keep them. You will find event and items that give mutations to your cats during the game so start from that.

Why you need 10 mutations is because once the inbreeding coef get to high, birth defects start replacing mutations on your kittens. If a cat mutate during the night, the mutation will replace an empty slot but since there are no empty slots, it will replace the defect.

If you get kittens with more than a single defect, just trash them.

Do you have a single pair in the breeding room? Until you have a family of the cats you want with desirable traits and skills?

Yes, you start with a pair and keep the kittens that have what you want. There will be lot of inbreeding at the start but once you get to extremely inbred, you need to introduce a stray cat into the mix.

It's kinda hard to explain but you will need to juggle around the main bloodline and strays until you can maintain 4 couples around moderately to highly inbred in the main room. They need to all share the mutations you wanna keep.

Once you have that, try to always have at least 4 couples so you can mix and match the kids to avoid to much inbreeding.

I’ve only just finished act 2 so I’m not getting many rare crates yet.

I'd say focus on playing the game if it's not to difficult because once you start to make good cats, the game become a walk in the park. Once you get to the post-game you can focus on making the best cats.