I want to grow brewers yeast that I want to as use as supplement, get various nutrients and NAD+. Which brewers yeast strain is easiest and best to to grow for this purpose? What medium and supplements for yeast I may need?
Pretty much 99+% of all yeast used in food and health products (from Marmite to yeast pills) is Saccharomyces Cerevisiae (i.e. beer yeast or bread yeast). A small part is S. Pastorianus (mostly used in industrial lager brewing). Wine and distilling yeast (S. Bayanus) is rare in the food and health market.
The best growth medium for beer yeast is a well-formulated, well-oxygenated wort. Brewers do this all the time when they make yeast starters. Make a starter wort from malt extract, add a good quality yeast nutrient (ideally one rich in zink and FAN) and continuously oxygenate the word for the first half of the fermentation (no shorter, no longer).
Let the wort ferment out completely and let the yeast settle before harvesting the yeast, because this will promote the build-up of nutrient reserves within the yeast cells.
Zamil Zainasheff's book on yeast is recommended reading for any aspiring yeast wrangler.