Looking for a good text on science of grilling and barbecue

I think grilling is probably a bad plan for duck legs; the fat content is a real danger like you said, and duck legs are tough enough you probably want to confit them or braise them.

If you absolutely have to grill them, I would suggest confiting them at 200 degrees for three or four hours first (you could use veggie oil in a pinch) and then resting them in the fridge for a day or so in oil.

As for finishing them on the grill, rinse them off gently, re-season if needed, cook flesh side down on a medium heat portion of the grill for a while until mostly heated through, then flip them over on a high heat portion of the grill to crisp up the skin, watching out for flares.

I notice Flank steak already made the list, and once I would have agreed, but it's gotten trendy, and with the trendiness, expensive. It's still not fillet-price, but it tends to run in the 7-8 dollar a pound range where I live.

The steak I like to grill that I find to be tasty, cheap, and available is skirt steak. Do a light marinade, grill it as lightly as possible, cut across the grain of the meat, serve.

Your mileage may vary, however. The cheapest cuts are almost always the ones that local cooks don't know what to do with, and if the locals are hounds for the fajita, you're not going to be able to find skirt steak at all.

My advice is to go to the store with an open mind, and browse the meat counter looking for deals. I came home with 3 pounds of tenderloin tips for less than twenty bucks the other day: if I'd gone out looking to buy such a thing, I'd have been disappointed.