I just moved into a new apartment, which has through-the-wall openings for air conditioners. I've never dealt with through-the-wall installations before; I've always lived in apartments where I could install an A/C in a window using the accordion sides to make it fit.

The A/C unit I have is this one, which is 15.72 x 18.59" wide x 12.75" tall x 15.72" deep.

The wall aperture is 26.5" wide x 16" tall x 20" deep.

So, the aperture is much bigger than the A/C unit.

Here is a picture of the problem.

I don't imagine I'm the first person to have this problem. My naive solution would be to cut out some cardboard pieces to fill in the space around the unit, combined with duct tape, but that will look like shit, and I think I can do better.

What's the best way to proceed?

If I want to build a sleeve out of wood to hold the unit, which would fit snugly and which I could paint/stain so it looks nice, I'm sure I could (badly) sketch it and calculate the size of the pieces I need with pencil and paper, but is there some application I can use to help me digitally "sketch" the thing?

Once I know what size wood pieces I need, would a place like Lowes or Home Depot be able to cut the pieces to size for me?