There are two great things about cheap cuts of meat. 1. They're cheap. 2. They taste better. Yes, they take longer to cook; but I find that something like short ribs or lamb shanks, cooked down for many hours, are much more flavorful and versatile than steak. A big pork shoulder will run maybe $1-2 a pound. Buy the biggest one you can.
Take the entire pork shoulder, skin and all, and pop it into a big cast-iron Dutch oven. Put some quartered onions and carrots on the bottom of the Dutch oven; maybe a little leftover wine, as well. Cover. Cook at maximum (475 or so) for about 20 minutes, then turn the oven down to 250 and cook until meltingly tender, 9-12 hours or so.
That's all you have to do. You can start this first thing in the morning and leave it, producing a wonderful entree for dinner. You don't even have to stay home--this doesn't need to be stirred, or flipped, or checked, and since it's cooking at such a low temperature, you don't need to worry about overcooking or burning it. Just throw it in the oven in the morning and take it out when you're ready to eat it. The skin and bones will fall right off the meat, and the meat will be so tender you can shred it with a fork. Serve with barbecue sauce, or a white wine sauce, or over white beans, or over braised greens, or whatever.
I've had great luck with this as a party dish, served with barbecue sauce. Sorry, folks--I may be willing to give up my bacon chocolate recipe, but my barbecue sauce recipe is a trade secret.
Cost: Last time I made this was in New York; I believe I got 8 lbs of pork shoulder for $10-12, and it fed...well, that thing could have fed 20 people. I served it at a party and was still eating the leftovers for days.