I prefer to bowfish for them. Its a blast to try and hit them. The water refraction is very deceiving. Granted you can't throw them back this way, but they make excellent fertilizer.
Use about anything for carp bait, worms, corn, corn cobs, dough balls, even bean pods. As for eatting them I have the best recipe, dig hole about 10 inches deep, fill in place tomato plant in dirt, some of the best tomatos you can eat. lol