The pinnacle of Pokemon to me I would say would be Pokemon Heart Gold and Soul Silver. For one, these games to me represent everything Pokemon is and what I love about the franchise. There's actually a thought I gave on what Pokemon means to me that I have written on my site's about page, and I think it perfectly describes HGSS: :)
"The first two generations of Pokémon games, to me, though containing simple, old, visuals, give a feeling like I'm adventuring, wanting to know about these creatures from ancient myths and stories, becoming friends with them, taking on a role of a hero, and aiming to be a champion, as if of a sport. It's all an adventure a child would love to go on. Pokémon is like some kind of grand journey. It's like a child's fantasy.
This is, what Pokémon is to me.
Other games would later be made in the franchise, and bring even more exciting experiences.
My goal for this site is to seek and discover the magic, wonder, stories and dreams of this amazing world, and tell its many stories and experiences the players can take part and interact with."
And beyond the games' adventures, the developers best take advantage of what to do with what you love about the world in its content: All the features (like competitive battling,) we can participate in with our favorite Pokemon and form memories and new chapters in our own logs, that are another one of the things that makes the universe like I made it out to be in my quotes.
To be honest, I don't know much about what it's like for these players to travel and compete, (could be partly not glamorous to a certain degree,) but I imagine it must be something to see different parts of the world, (being cities and landscapes,) meet certain people you like, battle competitors with same interests as you, and fight alongside favorite Pokemon. All to form "Your own story," as they say in the games.