Pokémon Heart Gold (or Soul Silver). Just because when it comes to getting the most out of a Pokémon game, this game can really give you the most out of a Pokémon game.

You have two regions, Johto and Kanto, and you can catch upto 4th Generation of Pokémon. Two regions is what other games don't even try to do anymore. You can choose the 1st gen starters, and go against the gyms and the Pokémon league of Kanto, in a game about a Johto story. Go figure. You get to use the Squirt Bottle, the Poké Flute and there's a side story about Slowpoke poaching, Team Rocket's prominent, this game is bananas and I love it when Pokémon tries to do these things. It's a world with sentient build-a-bears that can fart lightning, things should get weird. When it comes to catching them all, this game lets you catch them all (upto 4th gen of course), there are many events for different Pokémon like the Unown and the story is the classic Pokémon story. The animations in battles are quick and snappy, while the cutscenes are less frequent so it the game doesn't waste to much of my short Earthly years with too much exposition.
One of the best parts is, Pokémon actually follow you outside of their Poké Ball when free roaming.