circles on screenshots that move with the screenshot

Edit your sceenshot into 'paint' before you paste it into Word. Copy/paste do 'paint', draw the circle in 'paint', copy/paste from 'paint' to Word.

Select the objects in question (SHIFT + click each item) then right-click on one of the objects, go to Group > Group.

When the objects are grouped, they can be moved as a collaborative object.

my own research and efforts have led me to believe that you can't group shapes and pictures.  Is the only way to accomplish my goal to edit in paint first???  The problem is that when I alter the document and the picture shifts down or up, the shape (a red circle) doesn't move with the picture.

Try right-clicking on the picture image and then Wrap Text > Behind Text. Make sure your circle or other shapes are set with right-click, Bring to Front > Bring to Front. You will see that you can Group both pictures and shapes fine now.

Maybe I'm just causing too much trouble and paint would be easiest.  What do you think?

After I right clicked on my picture and selected format picture and then layout and then behind text, all of the text that was below it moved up and is now on top of the picture.  I was hoping the spacing would remain the same.  I'm sure you understand what I am trying to do.  just wanting to insert pictures with drawings on top and have them shift together appropriately.  I don't think it is that bad with paint.