Yellow Version was, and always will be, a special case. In Yellow, you got a Pikachu as your starter and received each of the other starter Pokemon throughout the story. That's (probably) not gonna happen again. You still play through the same gyms and story.
The G/S remakes are enhanced versions of Gen II, with better graphics and story elements from Pokemon Crystal. Neither gives you "everything" of the previous two games.
A lot of people skip the first two releases and go straight to the third. I did it with Emerald. With Gen V, we got two sequels (B2W2), so now there's that risk. But generally, the "3rd game" will have a greater variety of (read: more old gen) Pokemon, different gym(s) and story elements, as well as some other upgrades.
The benefit of playing through two versions is that you can build a better (or just different) team the second time, giving you a different experience to go with the other changes. You also don't have to wait, and there's more legendaries to go around for you.
Hope that helps.