Which "Don’t Starve" expansion should I buy (first)?

Reign of Giants is basically the only expansion to the base game.

The others are their own thing and aimed at players who have already mastered it. They are not really so much expanding the base game as opposed to turning it into something somewhat different for the sake of variety.

I think they are all worth buying but definitely start with Reign of Giants.

RoG adds a lot of content which makes the early game a bit easier, and opens up a lot of possibilities later.

The other expansions are only worth it once you have "completed" RoG.