As for fats, I actually learned this week that the original variant of Canola (rapeseed) oil is a traditional cooking oil of China, besides pork/lard.
Rapeseed oil comes from Brassica rapa, which includes many common Chinese vegetables inc. cabbage, bok choy, and yao choy which literally translates into "oil vegetable" from Chinese. Canola is the Canadian version which has a lower acid content of erucic acid, but in traditional Chinese cooking my preliminary research seems to show that you use rapeseed (preferably now Canola, expeller pressed if possible) plus some saturated pork fat.
I recommend Wisdom of a Chinese Kitchen http://www.amazon.com/Wisdom-Chinese-Kitchen-Grace-Young/dp/0684847396/ which actually has ground pork butt (1/4 cup) in many recipes. Pork butt (actually comes from the shoulder) is a fatty cut, and a 1/4 cup has you using the meat not only for seasoning (umami) but for the fat.
Unfortunately, the American diet focuses a lot on beef rather than pork and it's much more difficult to get high-quality pork compared to beef. Anyway good luck and let us know how it goes!
My husband got Wisdom of the Chinese Kitchen as a gift from his great uncle and it seems pretty legit. I haven't tried any of the recipes yet because honestly they're a little intimidating, but just flipping through it, the recipes looked "right" if that makes sense.
Always end up making a big batch whenever I read one. It's kind of a PITA to make the cha-siu from scratch, though. The recipe I use is in this cookbook, but woksoflife's recipe is pretty good, too, and gives you more step-by-step. :)
It depends on what type of Chinese food you are looking for. For Cantonese, I love Grace Young. Her Wisdom of the Chinese Kitchen gives me so many great flavors and memories from what my grandma used to make for our family when I was little. She has other books that get great reviews, too, but this is my go-to that I ALWAYS turn to when I am craving food that reminds me of home. It has a really good array of everyday basic cooking to celebratory (Chinese New Year) to healing tonics/soups and even a decent number of Chinese desserts.
For a variety of Chinese food, Fuchsia Dunlop is a great resource, as she delves into the history of the foods as well as the nuances of regional cuisines. Her Land of Plenty is delicious for Sichuanese, and her Every Grain of Rice showcases delicious, authentic dishes from all over China.