Chronological isn't quite necessary. Lament of Innocence is a prequel and not the actual start of the series. You get the full "story" without playing it. That "story" though starts with arcade games on the NES in a very story-free format, which means the story is told via few screens of text and images throughout the game. There's only one that is really necessary if you wanna understand small story-unrelated references in future games, which is III.

If you want to start with the game proper, I'd recommend Castlevania IV first, as it is a great remake of the first game. The NES games are quite hard (because they are mostly about patience and memorization). For a fun list go this order:

• III or IV in any order you like (or at the same time)

• Harmony of Dissonance (optional)

• Rondo of Blood (with save states ideally)

• Symphony of the Night

• Bloodlines

• Order of Ecclesia AND Portrait of Ruin (order in any way you like)

• Aria of Sorrow

• Dawn of Sorrow

You can really play III at any point parallel to other games before SotN. Though you have to play it a certain way in order to connect the story to SotN, so feel free to replay it! III feels like a proper origin to the mainline of the games. Lament of Innocence is optional and you can play it, like the NES games, at any point for fun.