Around the mouth, upper lip and smile lines. How many units do I need? (Photo)

While small doses of botox can be used to weaken contraction of the sphincter muscles around the lips, this will not affect the static wrinkles, noticeable in photos and when your muscles are at rest.  These are best treated by resurfacing (lasers, chemical peels, or dermabrasion) and fillers.  Several small particle fillers have been developed to try to efface these fine lines (Belotero, restylane silk).   Consider a formal consultation with a Board Certified surgeon to discuss your options.  Best of luck.

Thank you for your question and for sharing your photograph.  Botox works best on dynamic wrinkles, those that develop as the underlying muscles of our face move.  The wrinkles you are most concerned about appear to be static wrinkles, present even without animation and would best be treated with dermal fillers, as wound your smile lines where are facial creases and not wrinkles.  Depending on your desired cosmetic appearance I would recommend a full face and neck lift, but if you are uninterested in surgery you can achieve a less dramatic improvement with fillers.  Hope this helps.