The Magic Beast family is interesting, but you can generally ignore it since the only Weapon that deals extra damage to them is the Excalibur, which you're going to be using whether you're fighting Magic Beasts or not.
The Magic Beast family is a strange one. Even if family weaknesses worked in the game, the only Weapon that is powerful against Magic Beasts is the Xcalber, which you're likely to use regardless of what you're fighting.
The Magic Beast family consists mostly of unnatural, blatantly magical, and demonic creatures. It's quite a large group, and both the Demon Spear and Wing Sword will serve you well in the middle of the game when you find them.