A fellow keeper kept 6 in 3x3 coop with good height, with no issues. I personally would lay it down and do a 3x8 coop. People have reasons to do what they do.
Take all the "rules" with a grain of salt. By rule, 2x2 coop is OK if you have one bird, and 4x4 coop is going to harm a flock of 6. Well, neither is true.
Bigger coop is always better, but budget, space, esthetic constrains may dictate otherwise. For your flock, consider 4x8x4h. If you wish not to have to step in the coop, I would suggest 3x6 footprint which you can reach in and get to every corner.
Run should be as big as you reasonabily can make it. Make sure the cover can hold snow load.