Honestly, the chronology gets a bit messy. Start with the original core quartet: 'The Awakening', 'The Struggle', 'The Fury', and 'Dark Reunion'. That's the main story about Elena, Stefan, and Damon in high school.
After that, the timeline branches. 'The Return' trilogy ('Nightfall', 'Shadow Souls', 'Midnight') is a direct sequel set after 'Dark Reunion', but it introduces a whole new mythology with the kitsune. It's good, but tonally different. I'd read that next.
Then you have 'The Salvation' trilogy ('Unseen', 'Unspoken', 'Unmasked'), which is another modern continuation, and the 'Stefan's Diaries' prequel series. The prequels are fun for Damon fans but not essential to the main plot. My advice? Core four, then 'The Return', then 'Salvation', dipping into the prequels whenever you want more backstory.