I would guess a Pokemon Ranger game. I've been meaning to do a Ranger run myself, so if you are doing it..Darn, you'll probably start before me. xDD
And I'm going to guess you'd pick Guardian Signs.
Here's my reasoning:
You did not rule out Ranger in this thread. It is within the 1-5 Gen range. Latios and Latias make a big appearance plot-wise in-game. And it would be really fun to Nuzlocke, in my opinion. :D
However, I'm probably wrong. Because:
You mentioned Trainers and a Rival's starter. Ranger does not have these. The poll helped choose the game, and I don't know how many people would have voted for Ranger. And I'm not entirely sure randomizing a Ranger game would work, considering the obstacles and such...