Your bit should very lightly touch against the corners of your horse's mouth. It should not hang out on either side, and it should not appear to be tight against the sides either. That is with you standing in front of the horse and pulling the bit from either side so it is taut.
Many times if a horse is getting their tongue over the bit while the bit is the correct size, it is because the bridle is adjusted incorrectly. The cheek pieces should not gape away from the horse's head when you pull on the bit from either side. The bit should sit high enough in the horse's mouth that there is a very small wrinkle in the corners of the horse's mouth. Otherwise it may be hanging down too low.
As far as choosing a bit...that is more complicated. It depends on the stage of training your horse is in, what they have been trained with in the past, what discipline you ride, etc. It never hurts to begin with a basic snaffle and go from there.