Hi, welcome to the forum. Glad you joined.
You might follow the link in my signature below to see some of my thoughts about space. There are no magic numbers with chickens. We are all unique in so many ways that what works for one may not work for another. We have so many different flock make-ups, goals, management techniques, climate, schedules, and so many other things that our actual requirements are different. If we could even agree on what numbers are magic (and we can't) they'd at best be considered guidelines, a place to start. And it's not like at 9.99 square feet per bird you are guaranteed disaster while at 10.00 square feet live is heavenly. It's more a matter of degree. I find the more I crowd them (and I sometimes do) the more behavioral problems I have to deal with, the harder I have to work, and the less flexibility I have to deal with issues. The more room you can reasonably give them the easier it is on you, which means it is also easier on them.
Some standard numbers given on here are 4 sq ft in the coop and 10 sq ft in the run per bird. For some people that is plenty, for some not enough. If you have a mature flock of hens that are already integrated it is usually more than the bare minimum necessary but you say you want to integrate in the future. Integration generally requires a fair amount more room.
Another thing is that chickens don't think in terms of coop or run in isolation. If they need room they don't care where it is as long as it is available.
I don't know how you are building your run or how much room you reasonable have to build it. With some building techniques it can be expensive to expand, others pretty easy. In general, for coop or run, if you are buying standard construction materials many come in 4' or 8' dimensions. You can often save money, cutting, and waste if you incorporate those dimensions in your design. 6' in a coop isn't that bad. The cut-offs can often be used to make nests or something like that.
I also consider raising a small coop and using the area under it to be a good idea for many reasons. And I strongly agree that you need access.
Good luck!