Buying shellfish alive is the best guarantee of freshness. Look for moving legs, claws, antennae, and, in the case of lobster, a flipping tail.
Stone crabs and king crabs are usually sold cooked―sometimes frozen, sometimes thawed. A live-cooked lobster will have a tail that curls back with a snap. These are all best served cold, since reheating toughens the meat.
You can keep live lobsters and crabs chilled and moist (covered with water-soaked newspaper) in the refrigerator for up to one day.
Plan on one one- to two-pound lobster or four to six hard-shell crabs per person.