In my opinion, the storyline of the first version (Red/Blue Rescue Team) was the best. It was a pity that it ended that there wasn't a real story anymore after the main storyline, but mostly some sidequests that gave you the chance to get various legendaries. The difficulty level was freaking insane.
The second installment (Explorers of Time/Darkness/Sky) had a good story. I wasn't full of it, but it wasn't bad. The treasure boxes and the outlaws were nice adds. I can't help to think how great Red/Blue Rescue Team would have been with outlaws... But oh well. Spinda's Cafe in Sky was okay, but nothing more. The recruiting system got a lot better. The challenges of legendary Pokemon were awesome. And then the bottles that washed up with their occasional hidden room mission, not to mention the so-called legendary items, like Golden Apple, Secret Slab etc, I loved it all. If I'm honest, I liked Explorers of Sky the most.
And the third...Jesus goddamn Christ, what did Mystery Dungeon ever do to you to deserve this, Gamefreak? Why? Good story, good sprites. And that WAS IT. No afterstory AT ALL. Only, idk, like 200 or even less Pokemon to meet, while the other two installments had all Pokemon in them. (that excludes Arceus in Time/Darkness/Sky) But this was just...oh god it was just bad. I never buyed it, and I'm happy about that after watching a YouTube walkthrough. The feels were horrible. Not like 'Oh I'm gonna cry' horrible, but like 'What the fuck did I just witness' horrible.
In my opinion, Gamefreak: take an alike storyline like the one from the first installment, not completely the same, but one that has alike elements, the mechanics of the second installment, and the design and sprites of the third.