Red/Blue/Yellow: are the easiest, and shortest games in the series and is nothing but the fundamentals of gameplay in the Pokemon franchise. Capture, battle, collect. Nothing more, nothing less. Hardly any extra features or sidequests. Your goal is to defeat the Elite Four, and become the Pokemon Master.
Gold/Silver/Crystal: added on many excellent features, such as night and day, two new elemental types, held items, more things to do/see, breeding, etc. They're all very good games. However, they have battery life, and I have two Silver versions who have both hit the bucket and will NOT save anymore. If anything, second generation should be the games you do NOT pick.
Ruby/Sapphire/Emerald: everything carried over, and there are some nice added features, but due to the battery life issue, night and day got the boot. This is where the battle system got a little more complex (natures, EVs, etc), and they refined it by adding many extra things like double battles. Pokemon contests now exists, which are something a little different to get into. Also, the best thing ever till you get your bike was added, RUNNING SHOES.
Diamond/Pearl/Platinum: added refinement to the battle system, refinement of the Pokemon contests, and other things across the board. Day and night returns without any hampering on battery life as well. Though not too many things were added, it improves on everything, imo. It also gives you the most bang for your buck, as it has everything from previous titles, a bigger region, and just more to do. Plus, you get wifi, which can make the gameplay experience even better.
It's harder to go back and play games once you play the ones that just came out, but it's hard to even find those said games at all (unless you count emulators). Also, not to shit on everyone's nostalgia and childhood, but Red and Blue suck now. This is coming from someone who was sickeningly obsessed with Pokemon back in '99 and had that obsession die before Crystal came out. The newer ones are better, and my absolute love for it back then would not cloud my appreciation for what it is now. Just. Better.
If you really want to experience the first games, get FireRed or LeafGreen.