My absolute favorite mammal has got to be goat. See cuts as for lamb.
Lamb: Shoulder cut, shank. Shoulder can be medium rare or braised. Shank should be braised.
Beef: I'm big on several of these:
> Bone in ribeye. (I don't see any point to the tomahawk cut, though - stupid long bone sticking out of it from which all the meat has been scraped off and wasted.)
> Hangar steak
> NY Strip steak
> Flank, skirt, hangar steaks.
All the above cooked medium rare, either in a skillet or on the grill. Thick cuts are great sous vide, with reverse searing.
> Korean-cut short ribs, made as Korean Galbi.
> Brisket, cooked all day in a slow cooker, with tasty seasonings.
> Tongue, which can be cooked several different ways.
Pork: Picnic roast, butt roast, country-style ribs. (These are all by the shoulder). Pork belly. Head cheese. Pork tenderloin sous vide for good temperature/tenderness control.