ME1>ME2>ME3 whoever says different is a degenerate
Degenerate reporting in
ME2 > ME1 > ME3
But if you break it down by categories
Gameplay:
ME3 > ME2 > ME1
ME1 gameplay is absolute shite. It doesn't know what genre it wants to be so it combines the worst elements of all of them. The shooting is total garbage tier, which is a problem since 60% of the game is spent in combat and every class uses guns. Shooting is stat-based and aim-based simultaneously, the worst of both worlds. The game begins with you untrained in shooting so even if you aim the reticule at the enemy you can still miss half your shots. Not because of recoil, but because the diceroll failed. Then when you get to a high level, you are now getting the worst autoaim hacks, to the point where you can miss the enemy by 1/4 of the screen's width and still land hits. The RPG mechanics are very simple, yet they still want you to invest in 50 levels of every skill available that only incrementally boost your power and the differences are hard to notice until you invest a shitload of points into it. There are a million guns in the game but actually there's only about 2 types for each of four categories, and they just vary somewhat on stats and what colour they are. Then there's the Mako, aka the worst vehicle in a videogame which drives like craps and fights like crap. The game has auto loot and party leveling and the inventory management is utter crap. Oh and it level scales like a motherfucker, although all 3 games have this problem to varying degrees.
ME2 takes a drastic approach where it just cuts huge amounts of the game. The Inventory was crap in ME1, so they axe it. Now you don't loot, you just pick up small numbers of unique items that there are no limits on. Once you get a gun, everyone can use it. There aren't 50 levels of each gun, just research upgrades to all guns of that category. There are a smaller number of skills with fewer levels, although they are more meaningful for each upgrade. Instead of 2.5% increase in blah repeated 15 times, it's 5 levels where one level you get a 20% boost, next level you get 15% cooldown reduction, and so on. It's a lot easier to notice the differences. The most important improvement is that they drop stat-based aiming. The combat goes from "utter garbage" to "serviceable Gears clone with powers". The persuasion changes are odd and I don't fully understand how they came to the decision to do it like that, but the addition of dialogue interrupts makes dialogue mechanics better overall. The abilities were changed from per-ability cooldown to global cooldown, which has benefits and drawbacks.
ME3 improves the combat a lot, and adds back some depth lost by ME2. More guns, they add back in weapon mods, there's grenades and heavy melee, and most importantly, they added a "weight" system in, whereby you can choose to take fewer guns and have faster power cool-downs, or lots of guns with slower cooldowns. Leveling system is the same as ME2, but with higher level characters there's a longer tree and more branches in the tree. Dialogue is a bit worse, not mechanically but they just did a worse job of building the dialogue trees. They feel more linear and have fewer interrupts.
Main Story:
ME1 > ME2 > ME3
ME1's main questline is the only good one in the series. It does unfortunately have a pretty sizeable plothole but overall it's a fun ride with a good villain. ME2 has a thin main questline, not that great, but it propells the plot forward and has a really satisfying final mission. ME3 starts bad, has some good bits in the middle, and then ends in a fucking insulting fashion.
Side Quests:
ME2 > ME3 > ME1
Loyalty quests in ME2 are way better than the side quests in ME1 and ME3, because they are a hybrid of main/optional. You can skip them, but they have a lot of love put into them and you're sort of not expected to skip more than maybe one or two of them. ME3 sidequests are "ok", ME1 sidequests are often thematically good but gameplay wise are pretty garbage especially if they're UNC ones.
Characters:
ME2 > ME1 > ME3
ME2 has the biggest cast of characters and has the best in the series basically. Wrex is the only other character from the series I miss in ME2. Mordin and Legion are gold and most of the cast is at least "solid". ME1 has Wrex and Garrus who are cool, Tali is ok, and the humans are Zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz. ME3 isn't far behind ME1, but there's nobody new who is particularly great. The closest is the optional DLC character, who despite being conceptually a terrible idea, works surprisingly well in practice (and should not have been DLC).