The "paired" games, released first for each generation, are basically copies of each other with slightly different pokemon.
The "third" game for each generation, that is, Yellow, Crystal, Emerald and Platinum, also have similar gameplay as the basic pairs of games, though there is usually more variation and they often add new gameplay mechanics or story elements. So going directly to the "third" games, like you're doing with Emerald and Platinum, is probably a good idea.
Obviously you're going to miss out on the GBA games, and the different (and probably inferior) gameplay they offer. If that's not a big deal to you, then no great loss.
So your order of play will pretty much give you an idea of the storyline of every game in the Pokemon franchise, as well as the catch-able pokemon.
Oh, and finally, you'll be starting out with a Generation 3 game (FireRed), going to a Gen 4 game (HeartGold), and then going back to a Generation 3 game. There's going to be a slight adjustment period there, when you go back to Generation 3's gameplay mechanics. It'll be like playing the sequel of a game first, before playing the first game.