I've significantly boosted the amount of fish I eat (from about zero to now at least three or four meals a month) over the past few months. Almost all of the fish is fresh (or sold thawed after previously having been frozen).
When it comes to sustainability of the world's fishes, I'd like to be part of the solution rather than part of the problem, but it seems that many of the fresh fish being sold in my local fish markets are on the "avoid" lists in terms of at-risk species. The number of readily available "acceptable" fish species is small enough that it threatens to become boring very quickly.
And that's just sustainable species -- saying nothing about the specific methods used by the fishers to catch the fish.
What, if any, strategies have you been using when deciding which fresh fish to buy?