Inositol is a B vitamin that's excellent for the hair. Its not expensive and is available at any health food store, or online. Usually a 650mg. capsule is taken one time a day on an empty stomach.
I'd suggest healthy fat supplements. Specifically, fish oil (DHA & EPA), coconut oil (lauric acid), and gamma-linolenic acid, which is found primarily in borage oil and evening primrose oil.
I also take Vitamin D - I don't think it has any direct impact on the skin but taking a lot of it allows me to avoid the sun entirely - I think sun exposure, outside of Vitamin D, is only bad for the skin.
According to swmbo's dermatologist - BIOTIN - is some generally awesome stuff. It is a B-complex that she buys in the 1000mg caps and takes 1 or 2 per day (not sure which). Apparently its one of the best things for your hair skin and nails.