I've been playing pokemon since Ruby/Sapphire came out. I've played every single one that is currently out, and got ORAS on pre-order. If you're looking to get into the games, each one has it's best points.
(I haven't played Gen 1 - 2 enough to give a good opinion on them, so I'm leaving them out.)
Gen 3 (Ruby/Sapphire/Emerald)
This games are great all around. They have a decent pool of pokemon to choose from and not a bad story. The layout of the region is good as well and training isn't too bad. They're a good starting place for new trainers.
As for Firered/Leafgreen, remakes of Gen 1, they're alright games. I've mainly liked them for being able to play Gen 1 with better graphics. They're also a good start, but I wouldn't say as good as RSE.
Gen 4 (Diamond/Pearl/Platinum)
These games are some of my favorites. They have a good story, an average one for a pokemon game, but they have a lot of pokemon to choose from, along with training much easier to do with the Vs. Seeker. I've enjoyed these games quite a bit more than RSE, but what you pick is up to you.
As for Heartgold/SoulSilver, remakes of Gen 2, are extremely fun. You get to go to 2 regions, lots of pokemon, and an extremely good post-game (Post-game being Kanto and Red.). They're extremely good games, but on the market today they're quite pricey, $50 per game.
Gen 5 (Black/White/White2/Black2)
I didn't play these games very much. Black and White limit you do only 5th gen pokemon almost entirely, and I found it somewhat of a short playthrough. (Compared to platinum.) Black2 and White2 do fix the limitations, but there are so many places added to the map that I got lost a few times. I wouldn't say these are good for newer players, but they're worth a try later on.
Gen 6 (X/Y)
Even though these are the newest games, I found these extremely fun. You're able to catch ~600 different pokemon between the two games, giving a huge variety of pokemon. The story is alright, and horrible post-game, but it's an easier game than past games, so a newer player might enjoy these games.
It's also worth mentioning that the Mystery Dungeon games, Expectantly Explorers of Sky, are incredible games. They have a great story, a good change in pace from the normal Pokemon games, and just fun all around. If you start to get into the normal games, try looking into these games.
That's my 2 sense on each generation, I'd look into either getting Emerald or X/Y if you're a newer player, for I think you'll enjoy those as your first games much more than any other one.