Reading the books chronologically also helps. You'll understand more of the references and see how the books build on each other (https://en.wikipedia.org/wiki/Great_Conversation) e.g. Homer (Ilad) -> Virgil (Aeneid) -> Dante (Divine Comedy).
Modern translations are great too. You can always go back and read more "faithful" ones. Some good examples are: The Divine Comedy (https://www.amazon.com/Divine-Comedy-Dante-Alighieri/dp/0871...) and The Canterbury Tales (https://www.amazon.com/Canterbury-Tales-Retelling-Ackroyd-Cl...).
That said, the best approach may be: don't worry about it. Sure you'll miss things, but you'll get valuable insights too.