Which is best to use for wrinkles around the mouth, and whst is the average cost?

Hi Anna.  Wrinkles around the mouth could mean a few different things - fine lines at the edge of the lips (smoker's lines), deep creases that run from the nose to the corners of the mouth (nasolabial folds) or even folds below the chin (marionette lines).  All of these issues can be addressed in different ways, so posting photos or being more specific about the area in question would help.
Surgery, injections and lasers are all options. 

Wrinkles around the mouth are best treated with a combination of procedures including: Fillers, Microneedling, Laser resurfacing, Chemical Peels, Radiofrequency, Micro-Botox, etc. A series of treatments will be needed for best results. You will need an in-person consultation and evaluation with an experienced physician provider to determine which combination of treatments will be best for you. Cost will vary depending on the treatments, location, experience of doctor, etc. Best wishes.

Dear annavictoriamelzer,it is hard to tell for sure without an examination. A procedure my patients love involves a combination of juvederm filler along the lines and corner of your mouth coupled with a small amount of botox to relax the depressor angularis oris (DAO's) to reduce the appreance of the permafrown. I would suggest you to consult a board-certified plastic surgeon. Only after a thorough examination you will get more information and recommendations.Daniel Barrett, MD, MHA, MS 
Certified, American Board of Plastic Surgery  
Member, Am. Society of Plastic Surgery