I'm looking to do the same thing in the spring at the back of my new garage, a bit larger though at 8' deep. Yours will be done long before mine even gets started, as I'm at least 4 months from construction, so no real help for you. There is corrugated flashing out there to use at the brick wall to keep any water from getting underneath and I think yours looks to be a pretty simple build.
Here is a process for taking some new, shiny panels and making them look more rustic/rusty.
Will be giving this a try for the wall behind the cooker.