I am painting a bedroom, bathroom, and hallway that is currently bright red semi-gloss. I have a few holes I need to patch and a few repairs to tackle but after that, I'm sort of confused.

What should I clean and prep the walls with?
Should I prime them?
Should I use a paint with a primer in it?
Or should I prime them then paint them?

I am going to paint them Benjamin Moore "Vintage Wine" in an eggshell finish.

Also, the ceiling is black semi-gloss and I want to paint it a matte black. How should I tackle that?

Any help would be greatly appreciated!! Thanks!