Chop watermelon into bite sized pieces and chill. Meanwhile, combine vinegar and lime juice in a small bowl. Slowly whisk in the olive oil and season to taste with salt and pepper. Add sliced onion and let marinate while you prepare remaining ingredients. Combine watermelon, feta, mint, and arugula or spinach (if using) in a large bowl. Toss with the vinaigrette-onion mixture and serve.
To allow their flavors to fully develop, leave the feta, greens and vinaigrette at room temperature when combining with chilled watermelon