Base size doesn't matter anymore. Only unit type.
Also, I'm gonna bring a unicorn as one of my magical beasts, it is going to be a royal unicorn thou, which is a Monstrous Beast instead of beast, does this mean it should go on a bigger base?
Yes. If a base size isn't specified, you should use either a 40x60mm or a 75x50mm base. That is what Monstrous Cavalry are on, and
MC is just a ridden Monstrous Beast.