Here's a link to my coop which is similar to what you are planning. mine is also up off the ground but it's not movable.
I enclosed the space under the coop so it's part of the run and in the winter I put windows on the three sides to give them more shelter from the wind and being underneath they already get rain/sun/snow protection.
Mine is 4x8 and I already wish it was bigger, dam chicken math(especially this time of year when CL ads for chicks come out!!)
Most of the issues that I have with my current design are height related, as noted below. I'm vertically challenged but did not realize these would be issues until the coop was operational
Make the coop lower to ground. I placed it high enough that I could put a wheelbarrow under the edge beneath the big door and just sweep out the coop in to the wheelbarrow. This was not needed as I use poop boards and with poop boards the litter of the coop only gets changed every couple of years,I expected to change it more often but it stays dry and oder free so why change it.
Make the poop boards/roosts lower inside coop. I placed the nest boxes and pop door about 8" off the floor thinking of the deep litter method for my coop, but again with the poop boards I do/need deep litter. Because of the height of the nest box my roost and poop boards are a little high in the coop for me. One when cleaning the poop boards they are at eye level for me so it's a little tedious to clean. If I needed to get a hold of a bird everyone says to just grab them off the roost at night but with the high poop board I don't have much room to pull a bird through the gap between the poop board and the top of the big door.
So my suggestion is to think about the cleaning chores and if you'll use poop boards or not.