Along with that, for 6 chickens, how large of a coop will I need/want? How many nesting boxes and what sizes? What else is needed and what else should I consider?
As I am also not allowed to free-range the chickens, I need a large enough run for them. How exactly does that work? Do they always stay in the run or can I let them in my garden or my fenced yard from time to time? Will this make a difference on the size of run I need? How large should I make it? Any ideas on what will be best to use for that?
I'd recommend looking into sheds, either premade or a kit. For 6 chickens you'd want roughly 24 sq ft of floor space (so 4 sq ft per bird), though more is always better especially if you have stretches of bad weather where they don't want to come out. If that's the case going with 6 or even 8 sq ft per bird may be better.
For nest boxes, 2 is enough but 3 might be better... I currently have 7 chickens and sometimes all 3 boxes are occupied. My boxes are oversized, 15" cubed with a sloped roof rising to 24" or so - if you're going for minimums I would say 12" cubed is as small as you should go (bigger if you want giant breeds).
Other things to think about: roost bars, aim for 12" per bird in roost space.
If your laws say no free ranging then yes the chickens should be inside the run full time, though if you want to let them out on occasion I won't report you.

Run space should be a minimum of 10 sq ft per bird though if you can go bigger, do so, as I personally feel the minimum recommendation isn't big enough and can lead to behavioral issues. My birds currently get 60 sq ft per bird in run space but obviously that will change as I gradually add more birds.
I don't build so I had a fencing company come and build a dog run, which I then reinforced with hardware cloth and netting.