Vitamin D and Zinc are both excellent supplements for skin and are safe to be taken together. I would take anywhere from 2000-10,000 IU of vitamin D, depending on how much sun exposure you get. If you are unsure, I would go get a blood test to measure your vitamin D levels. You should be aiming for >40 ng/mL.
There is debate on how often you should be taking vitamin D. If you are aiming for consistent levels all year round, I would reduce the dosage during the summer and increase it during the winter. That way you are changing it according to sun exposure. Some people however, take a good dosage during the summer and then taper off during the winter, assuming they struggle getting vitamin D regardless of the sun, and want to mimic seasonal vitamin D levels.
I would take Zinc as recommended on the bottle. Zinc is a mineral and I am more concerned with you taking more than necessary, so I would take a bare minimum. RDA is 15 mg. Perhaps get a food log online that can chug out how much zinc you are getting from your diet, and you can supplement from there.
Last tip: perhaps you should start these a few weeks apart. You aren't going to know which is effective if you take them at the same time. Most people don't care and take both anyway, so that's your call.
