Socializing cats?

Hey, I have a 7-month-old Ragdoll cat who is currently being neutered. Four weeks later, a cat of the same age from the animal shelter will move in with me. Unfortunately, my little one has been living with me on his own for four months now. It really was the wrong decision to get just one cat. That's why I'm all the more excited when my shelter cat moves in. As for him, he's about Bailey's age and very well socialized because he lives with seven other cats. Their personalities make a good match. I'm just really worried about us introducing them, that it might not work out or something. I live in a three-room apartment. My room is big and is basically the main cat room with a big climbing wall and scratching posts. Then there's a big living room and another bedroom. I'm not sure yet which room I should put the new cat in when she arrives. At first I thought maybe in my room where all the scratching posts are, but that's also the room my existing cat spends most of his time in and he might not like it if it was suddenly closed. I'm not so sure about the smaller bedroom as it's not really decorated in an exciting way. I could put a scratching post in there for when we arrive, but it's not that exciting. And then I imagine it will be difficult when I leave the room to stop Bailey from going into the room with the new cat. He'll probably sit by the door and scratch at it. How do I know when the cats are ready to meet?