Which chemical peel (type or strength) would improve my nasolabial folds and marionette lines the most? (photo)

Fillers would be the
best thing for nasolabial folds. As you know, the results are immediate and can last for a few months to over a year, depending on what product is used. It's best to fill in the lines
rather than try to peel them away.Lasers are also an excellent treatment option when it comes to
minimizing nasolabial folds. Lasers
will generally require several treatments but are highly effective especially
when combined with fillers. Personally, I have seen some great results with the
MatrixIR. It is a fractional laser with
no downtime, most patients only require 3 painless treatments.

These creases can improve with laser skin tightening, possibly, or a medium peel. Fillers are highly recommended, though.

I would not recommend a peel above 35% TCA.  Fillers are really what you need for your lines.  Stick with surgeons and physicians in the core aesthetic specialities like Dermatology, facial plastic surgery, plastic surgery, and oculoplastic surgery.  Don't go to a spa for these services.  Less is more.

A chemical
peel will exfoliate the top dead layer of skin, improving the tone and texture.
It will not improve your “creases”.

I would
recommend Belotero. Belotero is a Hyaluronic Acid filler, its molecule is cross
linked to better integrate into your skin and mold to your facial contours making
it an excellent choice for superficial lines. Like the “creases” that drive you
crazy. Belotero will give you immediate smooth and natural results that can
last up to 9 months.

Consult with
a Board Certified Dermatologist to see which treatment is best for you. For more information on Belotero click link below:

The best treatment for the lines in your skin is not a peel but rather an injectable filler like Belotero. I typically offer Jessner's or light TCA peels to my younger patients for maintenance of healthy skin. Deeper (35%) TCA peels are reserved for patients with more severe photo aging. 

I would not recommend a chemical peel regardless of the ingredient to treat the ectched lines. Belotero Balance is a filler that injected in the most superficial dermis. In time, the etched lines soften and blend more with the surrounding skin.