Play Black/White.
The Pokemon are all new so you can approach them all pretty fairly (some people view this as a bad thing but if you are going to get into new Pokemon, this is like jumping in the pool instead of wading in like a pussy), the mechanics are the best by far, and the story is the best (I did not say great, but it is the best: it is one of the few Pokemon games to have a cohesive and mildly compelling story. The final boss fight is actually REALLY cool).
You may be tempted to play Black2/White2. Don't. The story is lame and lacks the punch of Black/White, it derives most of its interesting points from how things have changed in the two years between Black/White. The trade-off is better post-game content and more Pokemon available, but if you don't like the game the first time through you aren't gonna want to stay for the post-game, and I am urging you to play without gen I pokemon because of the earlier pool analogy. Yes, you want to play with Pokemon you already like. But you will find new Pokemon to like, trust me.
Black/White are more straight-forward, no bull-shit games, and perfect introductions to the modern series.
If you really hold to your nostalgia, at least play FireRed/LeafGreen instead of Red/Blue, or Heartgold/Soulsilver instead of Gold/Silver. They are both tremendous improvements upon the source material while remaining loyal to what made the originals so memorable, and you owe it to yourself to not sell yourself short.
Have fun, OP!