I'm working through the game on my main but since this thread is popping I'll throw this out here:
I'm trying to pick an alt job to level when my friends aren't on, and currently thinking of Summoner or Black Mage.
How complicated is each's rotations?
Is Summoner a mobile caster?
I main SMN but also have level 80 BLM (though I haven't played BLM since I got it to 80).
Disclaimer: I don't play endgame contents that much and I didn't look up the 'proper' rotation for them.
SMN's rotation is more complicated with different phases. Regular->trance->bahamut->phoenix. SMN can be both mobile and stationary depending on the phases. Aside from dots(which is very important and much of your dps will come from them but there's not that much to talk about other than keep them up all the time), your regular spell is Ruin III which has cast time but you'll always have Ruin II that is insta-cast as an option. You also have pet attack (insta-cast) that share GCD but will give you ability to cast Ruin IV which is also insta-cast. Then you get into trance phases which makes your Ruin III also insta-cast making SMN very mobile. Then you get to Bahamut phase which turn you into stationary caster because Bahamut will move with you and won't attack while moving. Then the Phoenix phase is similar to Bahamut except now your Ruin is supercharged with Phoenix power. Then you are back to regular phase. It's a really fun class.
Most BLM spells have cast time. BLM is all about standing still for maximum damage so knowing the fight and know where to position yourself is very important. Later on you'll even have the ability to place ley lines which increase your spell speed so you will want to stand on your ley lines most of the time.
BLM's rotation is more simple. You'll generally have attack phase and mp regen phase. Fire spells have higher damage but cost much more mp while you'll regen your mp when you're in ice spell phase. So you'll switch between them all the time. Then you'll get to use some big spell after some conditions are met.