I skipped ahead to try Double Dragon and River City Ransom, since the collection had fairly easy achievements for both (beat level one of Double Dragon, eat all of the meals from the Sushi Bar in River City Ransom). Either I haven't played Double Dragon 1 before, or I forgot that it had a leveling system where you unlock new moves. (though I probably would have only known about the new moves part thanks to the manual in this collection)
I'm surprised at how forgiving River City Ransom seems to be, especially for an NES game. There don't seem to be any lives (at least, as far as I can tell) - if you die, you just respawn in the nearest town with half of your money (which can easily be regained by beating up thugs). By contrast, running out of lives in Double Dragon forces you to restart the game, and dying in Nekketsu Renegade Kunio-Kun forces you to restart the level.
I don't know if I'll focus on River City Ransom or the newly-translated Japanese version (by my understanding, they're basically the same game, with RCR being re-skinned for a western, or at least non-Japanese, audience), but I'll stick with one of those for now when I play this collection, and I'll likely pick up River City Girls when my next paycheck comes in.