I wanted to give an update on the situation since a lot has changed imo and other newbies should read this since I seem to have had up a common first impression. :-)
Firstly: Thank you all for your help - especially the people who helped with spell rotations.
I have been playing the game for 6 days now and BOY, did the job become more fun as levels passed by. I'm currently lv 46, didn't really rush (taking my time with the story and site-seeing while not being on a "road to 70" server) and Black Mage is already the best mage class I have played in any game so far. There are two reasons for that:
1.) You constantly have to manage your fire/ice stance later on which becomes a lot less annoying thanks to later ice/fire spells pumping you up to ice/fire attunment 3 instantly (which in the case of fire attunment 3 works literally wonders for my damage)
2.) The passives that BLM get are downright gamechangers. You constantly get to cast Fire3 and Thunder spells for free without cast times which pushes the damage even higher. The amount of explosions and thunder i summon is already huuuge at lv 46. While I didn't see my impact in dungeons before, i sure see it now.
3.) I had a peek at spells and passives to come and OH BOY is this gonna be good. Zooming around the battlefield, even bigger explosions and added BLM mechanics will make me VERY happy that I stuck with this class.
4.) The dungeons get (of course) a lot more interesting and managing my spells while dodging stuff is really taxing but also very rewarding.
If you started BLM and found it feels kinda boring, trust me: It gets A LOT better very fast.
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So I'm playing blackmage and nothing makes sense to me. I'm supposed to be a damage dealer but when I did my first dungeon a minute ago, it felt like torture because my impact was abyssmal. We had a paladin (so defensive tank, right?) who just killed everything on its own and I was standing there casting some fireballs and felt like a total idiot. Every minion feels like a grind in general, the casting is always the same and feels waaaaay too slow (considering how much damage my spells do).
Maybe I have chosen the wrong class? I looked up what BM is going to get (in terms of spells) and they all read the same (saying very bland).