Because their flesh is so easily damaged by their own enzymes once they’re dead, crustaceans are generally sold to consumers either frozen, cooked, or alive. Most “fresh” raw shrimp have been obtained frozen and thawed by the store. Ask for a sniff of one, and don’t buy if you smell ammonia or other off-odors. Cook them the same day.
The larger crustaceans, lobsters and crabs, are generally sold either precooked or alive. Live crustaceans should come from a clean-looking tank, and should be active. They can be kept alive in a moist wrapping in the refrigerator for a day or two. Relatively small lobsters and crabs will have finer muscle fibers and so a finer texture.