Chicken is cheap now. But that is a function of the massive industrial methods used and the odd breeds used to manufacture meat. Use it all you want, but I think that cheap chicken will go to the way of the dodo. I still laugh when I was reading an old cookbook from 1913 and they were giving a chicken recipe. The upshot was that they understood chicken was expensive, so if folks wanted, they could substitute a cheaper meat like veal.
Anyway, back to piggies. Buy the least processed pork you can find. I have found that sirloins from the restaurant store are cheap and can be cut up and put away as you need. You can also core out the good bits for grilling and leave the lower quality cuts for cooking.
Don’t be weird about fat on the pork. Make sure you get your pork from the cheap cuts and you can render the fat yourself for come killer cooking oil. Cut off the fatty bits from the pork, chop it into small pieces(less than 1/2 inch) and put it in the pot that you are going to be cooking the chili in. Set the temp as low as your stove can manage (or just use a crock pot) and give the mess a stir every five minutes. Over the course of an five to eight hours or so, you will get a clear oil in the bottom of the pot. If you are feeling really adventurous, toss in whole garlic cloves and some onions and let it cook with the fat, this flavors the fat in a very good way. When you have this all cooked down, toss out the chunks, strain it though a fine sieve, and store it in the fridge for cookin'.
This is the start of the chili-making process.
The rest of the pork needs to be cut up into the size chunks that you want in your chili. My rule of thumb is that the size of meat chunks in my chili directly reflects my financial condition. I keep the number of my meat chunks pretty constant. If I am feeling rich, they are big. If I am poor, they are small.