Pokémon: Gen 1. They are the ones I grew up with and known the longest. I love the Pokémon in every generation, but overall, gen 1 has a lot of my favorites, like Bulbasaur, Jynx, Onix, Ninetales, Jolteon, Growlithe, and many others. Pokémon wouldn't be where it is today if it weren't for the original 151 that started it all.
Starters: Again I'm going with gen 1. Same reasons as the last one I guess. Bulbasaur, Charmander and Squirtle are all among my favorite Pokémon. Especially Bulbasaur, my very first Pokémon
Legendaries: This one's a bit trickier. Jirachi is my absolute favorite, but then I also love Mew and Mewtwo, but then I favor the legendary beasts out of all the trios. Overall, I'm gonna have to pick Gen 2, because it's the one where I think I like them as a collective moreso than in other gens. Even then, tomorrow I might have a different answer.
Region: Another tricky one, haha. My answer has changed over the years, but right now I'm gonna say Kalos because of how expansive it is and the different caves and terrains that it has.
Protagonists: I like Red and Green a lot. I spent a great portion of my childhood playing as Red, who then ends up becoming one of the most powerful trainers in the world, which is pretty epic. And then Green/Leaf because I like her design, and I like her Manga counterpart.
Rival: I'm starting to feel like a genwunner, but Blue. He is a little bit of a jerk with an ego, he is always one step ahead of you, he becomes the champion, in FR/LG he uses a Tyranitar (which is awesome) and becomes a gym leader, without a type theme might I add. Plus he's Prof. Oaks grandson which is cool.
Professor: Prof. Oak...
Gym Leaders: so this one is a little hard to decide. I love the gen 1 gym leaders, but in later generations I liked how they gave them more to do, like in Gen 5. So I'm gonna say that as far as just their designs and characters, gen 1, but how the games handled their role in the story, gen 5.
Elite Four: Gen 2. Well, more like HG/SS. Will is cool looking. Koga's promotion from Gym Leader to Elite Four member was pretty cool at the time. Bruno is just Bruno, haha. And Karen's well known quote about using Pokémon that you like is fantastic.
Champion: I like Cynthia. I feel like she has the most diverse teams.
Evil Team/s: So, I have a soft spot for Team Rocket, however, I think Team Plasma takes the cake as best villanous team. They were a great part as to why Black and White had such a good story.
Plot: B/W. Most compelling story for sure. I never played Pokémon for the story, so I was pleasantly surprised when I played White. Also, I'd like to give an honorable mention to the Mystery Dungeon games, specifically, Explorers of Sky.
Music: All of them. I'm not choosing, I can't.
New/Improved Mechanic: okay, so I would have said the day and night system introduced in gen 2, but I can't. Mega Evolution completely took the cake. I love it, it made Pokémon new again (at least for me) and I'm looking forward to see what other Pokémon will get them in the future.
I'm like emotional that it's been 20 years since it came out in Japan. Time flies.