>>46473395In terms of pure narrative progression I would go...
Fire Red / Leaf Green -> Emerald (they take place around the same time)
Then Platinum -> HeartGold or SoulSilver
HeartGold/SoulSilver are sequels to Fire Red / Leaf Green, taking place three years later and continuing that story. But they were released after Platinum and improve upon its engine. They are generally considered to be he best games in the franchise, as they offer both freedom (which is in rare supply today, with Pokemon) and are feature-rich.
The Black/White duology was an attempt to elevate the series that ultimately ended in failure. Dramatic failure. But the duology itself is good. You will not be able to transfer Pokemon to Black and White 1 before beating the main story. You are limited to the Unova regional dex. But if you are using an emulator this isn't really a problem.
Be warned. The Unova regional dex is filled with ugly designs, and a lot of the cooler monsters are toward the back of the game. Black and White 2 correct this.
With all that said, I would treat this like a learning experience. Almost like a study of game design / of history / a study of a fandom. They're all the same game really, so if you're not following the plot, nothing new is really happening, and this is all to satiate your curiosity. I suppose it could be fun to see how the world changes, but the story is not nearly as interconnected or intricate as this post may make it seem.
The biggest observable transition happens between Fire Red/Leaf Green and HeartGold/SoulSilver. Black and White also references the events of the preceding games twice. But that's it. The stories are largely self-contained.