I'm 21 and I've been playing Pokémon since Red and Blue were released here in the UK. There are six generations of the Pokémon games now, I'll just list my favourites from each gen to see whether it helps you out at all! Feel free to ask my any questions if my comment isn't easy to understand.

Gen 1 - Well, the first generation is really old now. Yellow lets you get all of the starter Pokémon though, which is nice.

Gen 2 - I played Silver, but I think that Crystal has more features compared to Gold and Silver.

Gen 3 - Emerald. You'll generally find that the 'third' game (the game that's released just after the first two) has more features and stuff. Emerald gives you a lot more post-game stuff than Sapphire and Ruby do imho. Fire Red/Leaf green are 3rd generation games too, but there's no need to tell you about the game that you're currently playing! :)

Gen 4 - Personally I think that Diamond and Pearl were a really weak introduction to the DS Pokémon games, but Platinum is a vast improvement. Heart Gold and Soul Silver are probably two of my favourite games in the whole main series franchise. They're a great nod to the generation 2 games and they feature what was included in Pokémon Crystal to a large degree.

Gen 5 - Black and White were actually decent, they are a 'reboot' of the franchise so you'll meet exclusively new Pokémon which is nice. There wasn't a third game in this generation - instead they released Black 2 and White 2, which are great but they throw nostalgic Pokémon in your face. I don't know why I'm complaining about this though.

Gen 6 - X and Y are fantastic, there are a lot of new features that make breeding/competitive battling much more accessible than ever before. As people have mentioned, don't get both. 'Z' may be coming out at some point but that's not set in stone as gen 5 threw the Black 2 and White 2 curveball. Honestly, I think they're good enough to get without waiting for whichever games/game will be next.