Combat in this is really, really fun.
Strong advice for newbies: Just blitz through the early part of the game with laser focus. If your eyes glaze over at all the numbers, symbols, and advice, don't worry about it, just keep pushing.
The auto-battle is good enough that you can just use that for awhile and observe how it fights. Take control now and then to experiment, and once you get a handle on the combat, the rest starts to fall into place (cards give abilities, elements oppose, and you can power up your job and your cards).
Oh and don't bother 'chasing' the dragon around, bosses like that move around the map forever, you can chase them later to farm them for specific upgrade materials, but you don't need to worry about that for quite awhile.