Don't listen to the gen 3 haters, it's actually (one of) the best gen(s).
Well it's in my top 5 for sure!
But yeah, I'd say go FR/LG (either or), Emerald, HG/SS (either one), Platinum, B/W (either one). I'm not sure how much you care about, well... anything but I'll give a quick summary of a few things.
The original Gameboy games were Red/Blue/Yellow and had a ton of problems/glitches. They're still fun though and if you want them for history, I won't stop you, but keep in mind that Psychic stomps everything, and you can't transfer any of your Pokemon from these games to the newest games. If you insist on playing a pure Gen 1 game, I'd say go with Yellow since it hasn't been remade and it has a few nifty additions.
The Gameboy Color games were Gold/Silver/Crystal. They fixed a lot of the problems of the GB games, as Psychic didn't dominate anymore and there wasn't a plethora of glitches. Again, they're really dated and I'd recommend not playing them as your Pokemon can't be transferred, but the games can still be fun if you're not picky. I'd recommend Crystal if you insist on playing, but most of what made Crystal special was implemented into HG/SS anyway.
The Gameboy Advance games included Ruby/Sapphire/Emerald/Fire Red/Leaf Green. These are the first games in which you can (hypothetically) transfer all of your captured Pokemon to newer generation games. This will require you to own a DS/Lite, however, so keep that in mind. Of these, I'd recommend Emerald simply because the *minor spoilers* Team Magma and Team Aqua are exclusive to the other two games, but are both a part of Emerald. I'd recommend playing both if you weren't new to the series, but since you have so much to catch up on anyway, just go Emerald. Fire Red/Leaf Green are remakes of the GB games (Leaf Green=Blue for reasons beyond what you need to be told), but are updated with the mechanics of the new games. The glitches are mostly removed, balance is in place and if you didn't know RBY existed you'd never think the series had any issues. These days, RSE are probably the most skippable games. Gameplay is fun enough but the region kind of sucks and if I remember things correctly the only Pokemon unobtainable between all of the DS games are the Legendary Golems and they're not very good.
The Gen 4 DS games included Diamond/Pearl/Platinum/Heart Gold/Soul Silver. Platinum added a few new things, so you may as well go with that for Gen 4 games. The plot is mostly the same and there's only one Team this time so no real need to even consider D/P, just go Platinum. HG/SS integrate some mechanics from Crystal and Yellow as well and are my personal favorites despite liking them all.
The Gen 5 DS games are Black/White and upcoming Black2/White2. You can transfer anything from Gen 4 games to Gen 5 (and indirectly you can transfer stuff from Gen 3 to Gen 4, then to Gen 5). B/W was seen as sort of a revival of the series and you can see a TON of similarities from Gen 1 to Gen 5 in the Pokedex. A lot of the inspirations for the new designs are similar to that of the old ones, but they're different enough to keep most people happy.
tl:dr
If you're not wanting to get into things for the long haul, you can probably just jump in at B/W and enjoy the series enough. It's a sort of revival kind of like the new Doctor Who series, where the stories are sort of continuous, but you'll miss a few references and not know it and you can follow everything that's happening. The stories for the games, sans B/W are pretty linear, so don't think you're missing anything too deep. Honestly, I'd like to see someone who's not a little kid jump into the series at B/W and play sort of backwards to see how their opinions differ from people who grew up on the series.
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