Please remember that when the AC is on, the shutters MUST be pushed aside for good unrestricte air flow from the unit into the room being cooled.
Since most Window AC's Ive seen are extended a bit out from the actual hole cavity or window frame, the sides of the picture frame must be shimmed out so that the shutters close nice and smooth and without a bulge.
If you decide and plan to paint this project, I would get some nice grade pine 1X4's for the framing part. I would make nice mitre joints for that nice appearance. If youre not versed on mitre joints, then use "butt" joints which is merely butting the joints together. If you sand and smooth out, no one will tell, IF your painting them.
Then I would place a shim board, to raise the picture framing out from the wall to be one inch further out that the furtherest protruding part of the front of the AC. The one inch is for the shutters to close nice and easy and completely seal the appearance of an AC.
Now, the picture frame will need to be again framed in around the 1x4's since they are out from the wall. I would use something like quarter round or any type of dressed out molding that will hide and make the shimmed out picture framing look nice and neat.
Since you are doing all this work, I would be very careful NOT to disrupt the lean or fall of the AC in the window. I would even go on the outside and place a bubble level on the outer box to make sure its leaning down and away from the house. This is to ensure that the condensation will drip from the outside of the AC and not to the inside of the house. I am sure its OK, but good to check it out.
1X4's would be the wood size of choice and pine great if painting. If staining, then consider oak or birch.
I would lay out all my plans on the floor below the wall for "playing around' with. Then when you get the look, then lay this out on the wall. Molding is soo cheap and will enhance your project greatly. There are hundreds of cuts and types and this is what makes those mantels so nice.
After reading and digesting this, come back with your follow ups and questions, as we are all happy to help you.