Use a heavy pot for this. I use my 8 quart Le Cruset that I bought probably 25 years ago as a second from the outlet. The enamel coating resists the slight acidity of the chili and makes clean up a snap.
Do not use canned tomatillos. That will make the Baby Jesus cry.
I use La Victoria sauce. When I lived in Arizona, there was a local brand called Macayo that was outstanding.
You can use any fresh green chili, I have used Hatch, Anaheim, Pasilla, Poblano, and Jalapeños with great results. You can also buy the frozen Hatch chili’s in the freezer section, and that works well.
If you are concerned about the fat content, you can skim the oils off the top before you thicken it. I don’t, because, well, chili isn’t a diet food, it is supposed to be a comfort food.
You can use a slow cooker for this. In this case, brown the meat, and cook with the onions and garlic before putting the rest of the ingredients in to the slow cooker. Cook on low, for 8 hours and then thicken at the end in the slow cooker.
You *might* be tempted to cheat and use pork loin, as it is easier to prepare and cube (less fat/gristle and no bones), but I recommend against it. The meat from the shoulder cut is much tastier in this dish. Trust me on this.