I don't think I'm getting a picture tool tab (does it matter what version of Word I'm using? Mine's 2003), but following your instructions to look to the right, I found something that helped. On the main tool bar, there's a button that says "outside border" with a drop down menu. I clicked the drop down menu and was presented with a set of options for how I want the border to look. I chose all four sides and voila! I now have a border on all the images I like.

Thanks for leading me in the right direction.