It is difficult to choose the "best” treatment for periorbital wrinkles. Treatment choices include skin care, Botox/Dysport, Injectable fillers, Chemical peels, laser resurfacing, and blepharoplasty (Eyelid surgery). This is a great question to discuss in person during your initial consultation.
Are the wrinkles dynamic or only present with animation? Then, Botox or Dysport will relax the muscles and soften the wrinkles.
Are the wrinkles superficial or deep? Sunscreen and skin care can slow progression of the wrinkles and may help the appearance of superficial lines. Deeper wrinkles may require chemical peels or laser resurfacing.
Are the wrinkles due to loss of volume around the lower eyelid? If so, an injectable filler using hyaluronic acid such as Restylane can restore volume and improve the appearance of the skin.
Often a combination of these treatments is necessary to achieve a natural result. Good Luck!