Beef - the cheeks and braising meats (ribs, tail) are my favorites.
Lamb - i love the leg. I can roast it, brine and make a ham out of it, or braise it. Versatile on every cooking technique.
Pork - my favorite protein, period. I adore every cut of pork. But if i had to pick a favorite it will have to be the pig head (yes whole head; snot, ears, cheeks, perhaps a bit of the neck). Brine it for a week minimal, then braise it and turn it to tete de cochon (headcheese). Or tie it like a porchetta and braise it, then sear it to crisp it up. Or you can cure it over night with garlic, thyme and rock salt; next day just rinse and confit it. Then roast it in the oven for some extremely crispy skin and succulent juicy meat.
Offals are my #1 choice whenever i see them on the menu. No matter which part it is, i just love and admire it. It takes so much more preparation to execute it nicely.