So I started as a mage, but is there a path for me to become a spellsword?
Mystic Knight uses a combination of spells and sword/mace + shield. They're my favorite class personally. They focus more on using magical projectile cannons and buffing their own + party attacks with elements/extra damage etc.
At level 10+ you can change your vocation at Gran Soren's inn. Unless you have a very specific min/max build in mind, spend some time jumping around to all of the classes for a bit, they all have useful augmentation skills you can use across classes, some of them are really good for MK like stability while channeling spells, increased casting speed, etc.