You will need 4 sq ft inside floor space in the coop for each chicken. 6 chickens x 4 sq ft = 24 sq ft. MINIMUM. So that means you will need a coop - just the coop part, not a run - that is at least 4 ft by 6 ft. I highly recommend walk-in height.
Any nest boxes or feeders / waterers inside will take away from the floor space needed for each chicken, so why not at least start with 4 x 8 ft?
I cannot speak to insulation (not necessary where I live, as we have mild winters with maybe and entire 7 days of low 20 degree temps), BUT I strongly suggest you put a floor in your coop! And raise it above ground a bit, at least the height of concrete blocks, perhaps two of them stacked. This will give chickens a place to go for shade in the summer. Don't use just one concrete block, as I did, as this isn't tall enough for me to reach under there to catch a frightened chick.
For a run, the necessary space is 10 st ft per chicken, so you'll need 60 sq ft, which can be accomplished in many different ways: 6 x10 in addition to the coop. That is, you can't put the coop inside 6x10 space and still count it as 60 sq ft when most of it is taken up by the coop.
If the coop is used as part of the run perimiter, you'll have to cover/enclose the space beneath the coop, too.