What kind of makeup do you recommend for someone who had deep peeling done. What are some best brand in the market?

Ask the peeler. Without knowing exactly what you mean by deep peel or what was used, we cannot really answer. Your treating person should have made some recommendations, and if not you should call and ask. It is part of the treatment! Generally, something like Cetaphil moisturizer is well tolerated and can be dusted over with light powder like "mineral makeup". You can pay a lot for Jane Iredell or not.
BEST KIND OF MAKEUP. THE BEST KIND OF MAKEUP TO USE, IS THE ONE YOU LIKE THE BEST! TRY THEM ALL! GET SAMPLES AT THE COSMETIC COUNTERS. . .