Dear Pam, First, I agree: I still haven't gotten the "hang" of the messaging process, so I hope you get this! Since my primary sewing projects consist of slipcovers, I may not be the best person to answer your question. However, I have sewn garments over the years and, if I were making such a top, I would face the neck and arm holes only if needed to stabilize the area.
The whole idea of using a sheer fabric is to have a sheer look; obvious facings would look, well, obvious! Sheer organza would be a suitable facing fabric to use: it comes is several colors and is strong. However, you'll need to test sewing it on your machine since ultra sheer fabrics have a tendency to be pulled down into your feed dogs. Also, to prevent bulk, use pinking sheers for the outside edge of the facing. Again, if you feel the neck and armholes are stable enough with just the lining, forego the organza.
I hope this is helpful. Please stay in touch; I'd love to hear how this project comes out! Sincerely, Peg