What is the healthiest type of beans to eat?

Depends on goal. Lentils have high protein content. Cannellini beans have higher protein content, but also more carbohydrate and so for losing weight, may not be a better choice. Edamame has high protein, lower carbohydrate content, but soy beans have enzyme inhibitors which may block the action of enzymes for protein digestion. So, may be best to try 1/2 cup of lentils two meals daily, if trying to lose weight.
All. All beans are healthy, especially lentils - any type.