I don't think there's anything lost by not playing previous generations; just buy the newest games. All the newest DS games (Diamond, Pearl, Platinum, HeartGold, and SoulSilver) can connect to each other.
The battle mechanics were hugely overhauled after the "Advanced Generation" (Ruby, Sapphire, Emerald, FireRed, LeafGreen), so I would not recommend starting with those games. If you do, it will take a little time to adjust when you start playing the DS games.
Pokemon Red, Blue, Yellow, Green, Gold, Silver, and Crystal cannot connect to the newer games, so if you think you will become attached to the Pokemon you catch and train in them, it's not a good idea to start with them. Pokemon from the GBA games can be "migrated" to the newer DS games, but you need to have a DS with both a DS and GBA slot (the original DS and the DS Lite).
In short, I suggest you start with either HeartGold or SoulSilver, as those are the newest games.
Best Answer
I live in Italy and I own an English version of Pokemon Blue, but it doesn't have none of those designs. (I'm starting to think I own an American copy.)
This is a photo of the cardboard cartridge holder:
And this is the actual position of the cartridge in respect to the box: