Oh man, that's a classic rabbit hole. The straight publication order starts with the original four books by L.J. Smith: 'The Awakening', 'The Struggle', 'The Fury', and 'Dark Reunion'. That's the core story, and honestly, you could stop there and have a complete experience. The thing is, after those, it gets... complicated. There's a second run called The Return series, and then The Salvation series later on.
My two cents? Read the first four. If you're absolutely hooked and need more of the world, tackle The Return next ('Nightfall', 'Shadow Souls', 'Midnight'). I tried Salvation but it felt very different, more like a reboot with new characters. The tone shifts a lot from the gothic, moody vibe of the original novels, which is where my personal interest started to wane.