I would not limit your choices to a chemical peel. Various peels can be effective, but their results are often improved by starting first with an effective prescription-grade skin care treatment program.
Skin preparation should entail daily application for about 4-8 weeks. Use products that contain RetinA (trentinoin, not "retinoids"), hydroquinone 4%, and hydroxy acids. We use the Obagi system, under supervision of our aestheticians, including education and monitoring. Concentrations and frequency of application is adapted for each patient, and adjusted as you progress.
At times skin pigmentation problems improve very well with this treatment alone. If not, it is excellent preparation for subsequent peels or other treatments. Intense pulsed light (IPL) treatments may be more effective than peels.
So ask about some other alternatives and thorough skin pre-treatment.