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Since you speak of run height I am thinking you mean it to be covered? You will almost certainly have to go with aviary netting (or some similar substitute -- i.e. hawk- and chickenproof but not raccoon- or other-predator-proof) simply because of the engineering and expense of building a wire or solid top for a 500+ sq ft run. So you may want to start using 'search' to check out various ways of setting that up -- some, like the circus-tent-pole type construction, work best with a squarish run, whereas others, like using hoops or wires or lumber, work best with a longer narrower run.
As for coop size, as you know from your current chickens it is a tradeoff between the expense of building larger, and the aggravation of dealing with the consequences of more-crowded chickens (sanitation and air-quality management are harder, and you are more apt to have health or behavioral problems arise). So you have to pick where along the tradeoff you feel most comfortable.
You might consider building as large as you possibly can an open shed (with mesh walls, I mean, no siding -- like a picnic shelter, and only JUST high enough for you to walk in), then you can close in one corner somewhat for them to have protection from storms, and if you decide to close in more of it in the future you can easily do so... but in the meantime you'll have built as large an area of protection and shade as your budget will stand, and that's probably the most useful thing in the long run.
Good luck, have fun,
Pat