Resources for brands and ingredients from both Andrea Nguyen and Momofuku are very useful as suggested above, but availability may vary according to where you live and what Asian groceries exist near you. Beyond that, many products may be a matter of personal preference. I don't find any one brand to be excellent across the board.
Just a few of my favorites:
Peanut oil: Love Lion and Globe.
Red Boat fish sauce. Yes it's pricy but I don't use a lot of it.
Huy Fong chili garlic sauce. The most used basic Asian hot sauce in our house. I prefer it to Sriracha, generally.
Grandma chili crisp, the real brand name escapes me just now.
Blank Slate Sichuan chili oil. I order it from Mama Market
Wok Mei all natural oyster sauce. I like the taste. Don't get too excited it does say "Oyster flavored."
Mala Market brand Chinese Sesame Paste
SOY sauce: Although I really don't cook Japanese food much, my two current favorites soy sauces are:
Haku Black Garlic Shoyu. This brand makes several others that I've not tried
Peanut sauce: Jade brand, easily available in big supermarkets. I flinch every time a Chinese recipe calls for peanut butter. This Jade stuff is really useful, and it pack a punch. I use it for chicken stir-fry as an additional ingredient for a sauce.
Dry red chiles: I use a lot of Chiles de Arbol for various things. I also like the Mala Market Facing Heaven Chilis. The aren't that hot, but the have a very nice flavor.
Dried black tree fungus: I prefer the smaller more delicate cloud ears, but they aren't often available in the Chinatown markets that I depend on. So, I splurge on the ones from Mala Market. Yeah, Mala Market is expensive. They also have an extensive selection of Sichuan peppercorns.
Thee are a few off the top of my head. I'm not very adventurous; once I find a product I like I tend to stick with it.
