If you want to only play 3 games and have as much content as possible, then HGSS/BW2/ORAS is the way to go.
The content you get from these games are
>HGSS
Pokeathlon
Pokewalker
Gym Leader rematches
Customizable Safari Zone
Battle Frontier
Voltorb Flip (localization, Japanese versions have slots)
Local record mixing
>BW2
Medals
Join Avenue
Pokestars Studio
Musicals
PWT
Yancy/Curtis
Difficulty Modes
White Treehollow/Black Tower
N's Pokemon
>ORAS
working online with improvements (includes Wonder Trade, adding players as 3DS friends)
Amie and Super Training minigames
Easier breeding for online
Secret Bases (also improved from the originals, since it's online-based)
Contests
Dexnav
Online record mixing (Buzznav)
The content you miss by skipping the other games include:
>FRLG
Trainer Tower
The three minigames
>Emerald
Trainer Hill
Berry Blending
Game Corner Slots (if Japanese version this is something HGSS has)
>Platinum
Underground mining (Secret Bases are covered by ORAS)
Day/Night music
>XY
Trainer customization
Roller skates
For anyone wondering why I chose ORAS over Emerald, it is because the convenient teambuilding is much more important than the Hoenn Battle Frontier, since HGSS has its own Battle Frontier to use. Emerald also has its own restrictions, specifically when it comes to trading. You cannot play the game with any team you please, since Pokemon not in the Hoenn dex are locked out until you defeat Wallace.
