ME1: The draw of this game was being introduced to the world of Mass Effect, the alien races, the planets, technology, cultures, etc. Concepts like the Citadel, Spectres, and the cultural diversity of the races were all VERY compelling. It was purely a set-up game and there wasn't a lot of actual storytelling regarding the overarching plot of the series - we were introduced to Saren, learned about the reapers, and the established races accepted humanity by the end of it. I didn't think of it this way a lot before, but this game was probably the strongest of the three as far as story development.
ME2: Honestly, this wasn't great as far as storytelling is concerned. When I was just playing it again I was surprised how weak the start of the game felt. Like within 10 min Shep is dead, resurrected, and is now a member of Cerberus, who you spent a lot of hours fighting in the previous game. In that ten minutes, it was made pretty apparent that your choices in the first game were only going to have cosmetic effects from here on out. It felt very rough at the start. You went from being a hero to the Galaxy to a terrorist in a few minutes and your character is MOSTLY fine with that. The dialogue with Miranda and Jacob right off the bat isn't great (I don't know if I should trust you! But I guess I have no other choice! (YES YOU DO AND NO, THIS ISN'T AT ALL BELIEVABLE). It's all kinda shitty and beyond that, not much happens to advance the plot of the Trilogy.
The second game gets a pass for two reasons mainly - the gameplay was such an astonishing improvement over the first game and the character development was superb. This was the game that got you invested in your characters and crew mates more than any other. Overall story wise, though? Lets run through it pretty quickly: You die, get revived by one of your enemies, join them because "You're the only one who can save the universe and they are the only ones who understand that". You're given a ship and a couple of handlers and are told to gather a crew. You start doing that, find out humans are being abducted by ANOTHER unknown alien species - which is somehow way less concerning to everyone in the galaxy then every other time a new, agressive and advanced, species has made contact. But yeah, it's because you're a rebel now! You gotta do what the gov won't! You tussle with these aliens, go get some more crew members and do some loyalty missions, tussle with aliens once more, find a ship with some tech on it which will allow you to visit their space station in a different system, and then you go there and battle a giant human reaper. Somewhere towards the end you cut yourself off from Cerberus because they betrayed you (sort of). Nothing of import is really developed regarding the reaper invasion and what IS developed is handled very heavy-handedly. They basically destroy all the mystery and menace of the reapers and reduce them to a Saturday morning cartoon villain. Don't get me wrong, the game is great - super fun and everything, but the actual story development was sub par.
ME3 - Again a great game, but the story was a mess. Remember that time the one reaper nearly took down the galaxy? Well, now there's thousands, if not millions of them, as well as their minions and they're really not that much of a problem. You need to go out there and gather the 'ol gang! But only like half of it. You realize now that pretty much none of your choices mattered at all and just ended up adding resources that you could have gotten in a single mp match. Plot holes open up and literally everything is rushed in order to wrap everything up. AND WHY THE FUCK WAS THERE A GIANT HUMAN REAPER IN THE LAST GAME IF EVERY SINGLE REAPER IN THIS GAME (And there are a ton of them) is a giant squid or tiny reaper version of a race from this cycle? The whole fucking point was that they purged but curated the best DNA for their advancement. They just ignore it completely. And then the ending. Again, I love the game, but the plot wasn't really it's strong point.