I generally add a face frame to all my work. It not only adds to the width of the cabinet and is aesthetically pleasing, it also allows you to add some really interesting hinges.
Only solid wood should be used for face frames as the sides will show. The face frame also hides a plywood edge.
I leave a bit of an overhang so that I can sand it off flush with the side.
The face frame is generally as thick as the cabinet door when using doors that are flush with this framework.
With regards to these old window, it is best to use 1 1/2 thick material. So a 2 x 4 or whichever size you choose.
The vertical pieces that run up and down are called styles.
The horizontal pieces that run side to side are known as rails.
To keep these straight, just keep in mind that a rail road runs across the land. Not always but for this purpose it does 🙂