Welcome! We love new people!
I agree with Hens and Roos about having a grow out cage for kits (babies) after you wean them from the doe. If you leave the kits with the mom they will continue to nurse any chance they get. The problem with that is it delays the mom getting back into condition. It can make her very skinny, especially if it is a large litter. My grow out cage is 4 feet x 4 feet.
The hutches, or cages, for the individual breeding rabbits should be tall enough that the rabbit can stretch up. My cages are 18" tall. As to how big the cage is depends on what you are breeding. My bucks seem quite content with their 30" x 24" cages. My does who are not expecting a litter or nursing a litter also have cages that are 30" x 24". Does with litter have a 30" x 48" cage. Again, that works for my rabbits and their needs.
I don't think you need a run for the rabbits.
How about some pictures of your set up, please and thank you, once you get the rabbits all settled. We love, love, love pictures. Of course we would love to see pictures of any litters you have so we can ohhhh and ahhhh over the kits.
Don't hesitate to ask any question. Heck, if you are wondering about something rabbit then someone else may wonder the same thing or have worked through that question already. You are not alone.