I also would like to raise chickens to eat. From what I can tell, those will need to be kept separate with separate coop and run, correct?
If cornish cross, not really. Just a coop, or just a safe/covered run, not both. They're butchered when physically big but still young and stupid, so they won't go inside/outside reliably.
If you want dual-purpose chickens for meat, then a coop/run next to the first one might be a good place: raise the young ones, eat lots of males and some females, open a door between the two runs so the old ones and the new young ones can mingle. Having them side-by-side means they grow up with a constant look-don't-touch introduction.
If you raise the meat birds only in the spring/summer/fall, then you can let the egglayers have access to both spaces in winter, when the weather is more likely to be nasty.
Hatching eggs:
If you want to hatch chicks with broody hens, you could buy some bantams. The bantam hens can live with the full-sized hens and rooster most of the time, and then be separated when they go broody.
Why bantams?
a) bantams are more likely to go broody than full sized chickens
b) bantam eggs are smaller, so it's easy to sort which eggs came from which kind of hen. Collect eggs from the full-sized hens, then let the bantams hatch them.
If there are no bantam roosters, then there will be no half-bantam chicks from the big eggs.