First off, welcome to the front lines!
Kid Dracula, Haunted Castle, Judgment, and Harmony of Despair on PS3 and 360 are all skippable as they don't really add anything to the lore. Haunted Castle also is well known as one of the hardest (if not the hardest) entries in the series.
If you can, I'd suggest you give Order of Shadows a try. I feel it's worth a solid playthrough but, as it's a Java game that isn't distributed anymore on a platform that gets rarer by the day, you might have some trouble unless you can find a good emulator.
It doesn't contribute to the lore at all, but it's a rare story that shows more than one active Belmont at a time (three, in this case, though for equipment issues only one wields the Vampire killer, relegating the other two to a support role) and was about as good a Castlevania game as could be made for the platform it was on.
Also, while Kid Dracula is skippable, try it anyway. Both the original and the Game Boy port are quite good and clever little games.
Lament of Innocence on PS2 has a soundtrack and story that is widely considered among the franchise bests, though the gameplay is a bit repetitive. Curse of Darkness is one of my personal favorites, but you'd be forgiven by many for not finishing it--it ALMOST added to the lore by establishing the idea of Devil Forgemasters, Time Travel, and the vague future from which Saint Germaine claims to hail from, but none of its more interesting plot threads are ever picked up again, which hurts the series.
As for portable metroidvanias, they are all varying levels of good. If you play in release order, it'll be less aggravating (Circle of the Moon is non-canon but feels the most like the classic series, including difficulty).
Harmony of Despair literally adds nothing to the series. It just kind of "is" and is a Cooperative multiplayer entry rather like the new Star Wars Battlefront (no story, just chilling for a few hours in the franchise world with a few buddies). I wouldn't say it's bad though... just totally different (and admittedly cut-and-paste).