I've not played Ninja so I'm not sure how that plays, and I also hate Arcanist/Summoner playstyle so I don't recommend them.

I love playing casters but it really is a different play style and can feel painfully slow when you have to plant your feet and cast spells. If you want a class that is fairly mobile then go Red mage. With it's dualcast trait you'll have lots of opportunities to move around, and with it's gap closer and backflip you can move around a battlefield pretty smoothly.

That said, I do love Black mage as well but I know how painful it is when you can't get a single spell out before enemies die, please try not to let that upset you. Black mage has incredibly powerful spells and can put out some amazing DPS. At higher levels you'll learn the different abilities (triplecast, swiftcast, sharpcast to name a few) that help insta cast spells and give some movement to the class.