Neither microdermabrasion or chemical peels will remediate wrinkles. They help the skin look better though, because they exfoliate. If you want to do home dermabrasion, you can buy the corundrum crystals for cheap and just add them to your own facial cleanser. It's just like the kits. A real microdermabrasion shoots the crystals at your skin under pressure, so it's a little deeper exfoliation, and a lot more expensive.
Light chemical peels are nice...they make the skin feel very smooth. Hopefully the esthetician doesn't use too high of a percentage of acid.
I have done my own light peels at home, but I'm a daredevil. Lately, though, I find I get best exfoliation from just Retin-A, some light AHA/BHA acids and washing with a nubby washcloth. Retin-A keeps my skin at a nice level of exfoliation and keeps my pores clear, and it is just about the only product that has actually been clinically proven to eliminate fine lines and wrinkles.