For matters of seafood sustainability, I always turn to the Monterey Bay Aquarium's Seafood Watch. According to their list, the best shrimp are wild-caught from the US, and more specifically the US Pacific Coast and up into British Columbia. After my experience in New Orleans, I'd also add Gulf Bay Shrimp to that list.
Ocean conditions along the US coast are closely monitored and fishing is closed if anything harmful is found in the water. This means you can be sure the shrimp you are buying are safe to eat. Improvements to the trawl nets by US shrimpers also mean that there is less shrimping by-catch.
Domestic farmed shrimp is a good alternative. If possible, check that the shrimp were raised in fully-recirculating systems or inland ponds. These are better for both the health of the shrimp and the surrounding environment.
The only shrimp to really avoid is the shrimp being imported into the United States. Foreign fishing and shrimp farming regulations can vary greatly from US standards and you can't always be sure of either the safety or the sustainability of what you're buying.
You can buy either fresh or frozen shrimp; both are fine choices. Fresh shrimp is highly perishable, so be sure it's within a few days of being caught. The heads and edges of the shells will start to turn black as the shrimp ages, so make sure the shrimp bodies are translucent and moist with no black edges or spots.
When buying frozen shrimp, check for ice crystals on the shrimp. This is a sign that the shrimp were thawed and re-frozen at some point, and this shrimp should be avoided. You'll also sometimes see black spots on the shells of frozen shrimp, but the Louisiana Seafood Handbook mentions that this is due to an enzymatic reaction and not spoilage.
Thaw frozen shrimp in the refrigerator overnight and then use it right away. Frozen shrimp with their shells still on tend to be of best quality and flavor. (Plus then you get the shells to make stock!) That said, "peeled and deveined" shrimp are super convenient and still very tasty.
Big or small? That's up to you! Shrimp size depends on the specific kind of shrimp and is not in itself an indication of quality or sustainability.
In the wild and crazy world of seafood sustainability and quality, shrimp is generally one of the safest bets. As always, ask questions, check packages, and buy the best quality seafood you can find and afford.
What kind of shrimp do you buy? Any recommendations?
Sources for Seafood Information:
Related: What's the Difference? White, Brown & Freshwater Shrimp