Very intruiging questions.
If I can choose any badge from any canon then I would pick the Orange Island badges because they are so beautiful and have a more organic look inspired by sea shells, crystals and other treasures from the earth. My favorite is the spiked shell badge because its so distinctive. I also liked the Misty Meets her Match episode best of all the gym fights in that season.
If we're talking about just the games then I would say that the Kanto badges are the most consistent, they are each very colorful and fit the theme of the gym well. After much thought I would say my favorite is the soul badge.
Outside of the Orange Islands my top 3 badges from gens 1-6 are
Koga's Soul Badge- its so unexpected to make a ninja's symbol heart, but Koga was spiritual and graceful so I think poetic take on the art if war.
Wallace's Rain badge- I like the how the three parts come together, and one is filled with water and the other two are empty. The image is a little more complex then other water type gyms.
Valerie's Fairy Badge- it's so delicate and looks just like a pair of butterfly wings. It's perfect for her.