If I have three cards in hand (that includes Dunebreaker)... if I play Dune, would he enter ready or exhausted?

Yes, Dunebreaker will enter the battlefield ready in this scenario.

According to the ruling in RiftJudge FAQ #8756, this is a conditional passive ability that is checked at the exact moment the unit enters the board.

Sequence of events:

1. Playing the card: You start with 3 cards in your hand (including Dunebreaker). You play Dunebreaker.
2. Paying costs: You pay the energy cost to play the card. Your hand size is now 2 (3 cards minus the Dunebreaker you just played).
3. Entering the board: Dunebreaker enters the board. At this exact moment, the game checks the condition: "If you have two or fewer cards in your hand, I enter ready."
4. Condition Check: Because you have 2 cards remaining in your hand, the condition "two or fewer" is met, and Dunebreaker enters the battlefield ready.