1-Platinium first since its an expanded version of daimond and pearl no need to play those.
2-pokemon heartgold/soulsilver amazing remakes and for me the best pokemon games ever hands down.
3-black and white- new generation
4-black and white 2- these are the only sequel games, unlike older titles this is not an expansion but a sequel so play the original and the sequel.
I'd recommend Heartgold or Soulsilver, like many of the others here. Out of all of them on the DS, it's probably my favorite. It's got such a distinct vibe to it, not to mention my first Pokemon game was Pokemon Silver on the GBC, so it hits a very rich nostalgic chord with me. Although it does have a pretty sharp difficulty spike towards the end.
I know you're not looking for spinoffs, but it's still a great RPG experience all the same, though a tactical one, Pokemon Conquest is my favorite DS Pokemon experience. The gen 2 remakes are awesome too though.
Black/White 2 are actual proper sequels to Black/White, unlike the traditional "third version"; BW2 also have a TON more content than pretty much any other Pokemon game, previous or future.
I'd highly recommend BW2; they're the only games to have a Challenge Mode, to have the Pokemon World Tournament (where you can fight older Gym Leaders and Champions), to have the Black Tower and White Treehollow. It also has seasons and hidden grottoes (for the occasional Hidden Ability - most of the time it's just items, but when it's a Pokemon, it will have its Hidden Ability), for extra flavour, along with PokeStar Studios for a fun little distraction.