This seems to be a pretty typical problem. But reading many threads did not yet help me to find a solution.
I want to model a supposedly simple object. Unfortunately, the attached image is magnified. I have no idea how to make the image smaller. Looking at a smaller image makes it easier to understand the form.
I first tried to subdivide a base cube and model the cutouts, but this was not very successful.
The closest I came was using a boolean. However, I am not able to bevel the borders of the cutouts, regardless of the order of the booleans. When applying the boolean the geometry does not look too bad, but I still can't bevel the borders of the cutout, neither using a modifier nor directly.
I attach two .blend files: one with the boolean present, and one with the boolean applied. The design sketches can be found as empties in the .blend file.
Edit: @Chris. Your proposal did not help. This was my first idea as well. But if you look at the resulting topology after applying the boolean does not look too bad. I added another screenshot.