For acne scarring that's deep in the papillary and reticular dermis, we recommend trichloroacetic acid for a peel. However, the fractionated CO2 laser is generally a more effective and predictable treatment for deep scars. I would certainly consider this therapy instead of using a chemical peel.
It is important to know that glycolic acid and mandelic acid are unlikely to be helpful in the scarring that you've described, as they are meant for spa purposes. However, if you prefer a peel, consider a phenol peel. The weakest peel I would consider for deep scarring would be the V.I. peel, which is a mix of very low trichloroacetic acid and phenol.