There was a molding piece on the top where you could tell by the straight edge on the left side it had been cut apart and didn't match up with the curved cut of the right side. I decided that was an easy solution - just remove it. Two screws removed and it was done.
I then sanded the entire piece lightly to remove whatever sheen was left. (There wasn't much! This piece had been well loved or either really neglected!) I glued some of the peeling veneer back into place. I filled in the places where there was missing veneer with wood putty which was later sanded. Then, it was ready to paint. I used the leftover gray paint from my bathroom cabinet, Beauty. It's Home Depot's Behr paint in Rhino.
Here's one more look comparing her before and after.