The white and black are most likely your line (bringing voltage to the switch) and your load (bringing voltage to the light). You will need a neutral as well to use the GFCI switch receptacle. Please follow either diagram below, depending on if you'd like load to be GFCI protected or not, for proper wiring:
Thank you Eric for replying to my post so quickly...greatly appreciated. The info you provided was helpful. Unfortunately, I realize now my photos weren't bright enough.
I actually don't have two sets of wires, a white and black coming in from the bottom and leaving the top of the box, as shown in your very nice diagrams. Rather, there is literally only one black and one white wire coming into the top of the box and connecting directly to the switch screws - that's it. Nothing else leaving the box, only a total two wires (the white and black) connected to the switch screws.
I really appreciate any advice you could give me. Thank you very much.
There are two common ways to wire a switched light.
The first method (shown in both of Eric's diagrams) is to bring both the "Hot" (black) wire and common or neutral (white) wire into the switch's box. The white wire is passed on to the light fixture and the black one is connected to the "in" side of the switch. A black wire is then taken from the "out" side of the switch on up to the other terminal on the light fixture. Note: either screw on the switch can be the "in" side with the other one being the other screw. If your circuit were wired this way, it would be easy to add an outlet, using Eric's diagrams.
The second method of wiring a light (and the one apparently used in your light circuit) is to bring Hot (black) and the Common/Neutral (white) into the lighting fixture's box. The common/neutral is then connected to one side of the light fixture, and the hot continues down to the switch's box, where it is connected to one side of the switch. A wire, connected to the other side of the switch and is sent back up to the light's box where it is connected to the other side of the light fixture. Think of one wire, in the switch's box as being the Hot wire and the other one being the Switched-Hot. In this situation, there is no common/neutral wire in the switch's box. There is no way to add a outlet (GFCI or not) to this box. Not without bringing a common/neutral wire into the box.
Just a note about the wire colors in your photo. While white wire is normally the "common" or "neutral" wire and the black is the "hot" wire, the white wire is sometimes used as a switched (return) hot. This is simply because when using Romex (or the like) the cable has a black and a white. It is good practice to wrap some black tape around the white wire to indicate that it is really a [switched] hot wire. (Romex is a brand of "nonmetallic sheathed cable" (NM)0.
If "conduit" were used in the wiring of the house, instead of cables with two wires in it already, then both the hot-in and the switched hot could be black. And, for that matter, adding a white could be added for the outlet. But most codes do not require conduit. Some cities do require metal conduit (basically, a pipe) for residential wiring. I'm aware of Cook County (where Chicago is) Illinois and, I think, NYC requiring conduit.
From the photo, your cable look like it might be an older version of nonmetallic sheathed cable (NM).
So, the bottom line is that you would need a common/neutral wire in the box to do what you want to do. That white wire you see in your photos is not that.
Disclaimer: I am not a licensed electrician, but I have done a lot of wiring in my homes over the years - both with conduit and nonmetallic sheathed cable (NM).
If you don't have a neutral wire, you can't add an outlet, GFCI or not.
If you have one neutral, you can add the GFCI outlet, but not GFCI protect the switch.
(see diagram above).
To GFCI protect the switch, you need the light neutral to come through the box,
as indicated above.
Maybe not obvious, but you can use GFCI on circuits without a ground (green) wire.
You are supposed to label them "no equipment ground".