Jeez, ok I said I'd do this almost a week ago.
Better late than never, I hope.
Magic is tricky because I kinda want to go the D&D/pathfinder route of magic, but that kind of magic breaks story plots too easily.
For the terms of plot, I generally find if you remove teleportation, and long range scrying you're generally ok. But, I'll leave that to you. I will talk briefly about cultural development and D&D:
- you ever hear of the Tippyverse? You might want to look it up because it really hones in on how D&D magic would utterly mess up cultural development.
- The most important spells for cultural development in all of D&D are: Create Water (level 0 Cleric spell), Create Food and Water (level 3 Cleric spell), Remove Disease (level 3 Cleric spell). No joke, the vast majority of cultural and economic development is all based around scarcity of resources. The entire way armies developed as we know them today is the need for supplies. If you have magical resources that can just create food (or any matter from nothing, but food more specifically) you will mess up how society functions in ways that are hard to even comprehend.
Arcane magic (which was probably the most utilized) with enough mastery and knowledge can turn a single person into a nuclear weapon in terms of power, but it also depends on how they utilize their magic. I'd imagine that ancient kingdoms still had armies to fight with because they'd have mages built to counterspell other mages and vice versa.
You might want to check out The Malazan Book of the Fallen series, it did a bit with how magic will shape armies when it is possible to have mages that can destroy an entire army by themselves. I haven't read all of them myself but I enjoyed the two I did read.
As for what that means in warfare? Imagine storms with targeted lighting strikes being made and cancelled constantly in the middle of battle. Or turning the very earth into soldiers to do your bidding. Some low rank arcane users might be put on the ground to "buff" their soldiers (this is actually a dwarven battle Mage tactic I thought of. Basically every squad has a mage that specializes in artillery defenses and other protection so they can get their squad into the fight).
Well, a lot depends on what each of these spells are capable of. For example if the biggest thing an enemy mage can do is summon lightning, I can see armies transitioning to smaller, but more thoroughly equipped soldiers with steel from head to toe to act as a Faraday cage. That can be done with just a mail hauberk and footed pants.
Here, I'm gonna link you to something: https://www.youtube.com/watch?v=zwb7b9Ks0VE&index=49&list=PL2FCD81A6FE4280AC
I think this guy really gets how magic should be used in stories. That one, and the lecture just following it has some bits on how magic develops cultures, but not as much as I would like. But really, if you really want your setting to make sense, write down every single thing that your magic does. How common it is, and so on. If it's very common it will have far reaching effects.
I mentioned food and water above. But transportation is important as well. Does the magic create energy that can be harnessed (you mentioned lightning earlier) the dwarves control ground, so how does that shape the way their homes look (if it's really common do they even have doors or do they just knock down a section of wall and then put it back up every time they enter a room?).
This is not an extensive list but here's some questions you might want to ask with each magic trick:
-Does the magic effect how many people can live in a city (food, water, disease, cleanliness)?
-Does the magic effect how long it takes to travel?
-Does the magic make resources more useful/desirable? (ex: aforementioned metal for faraday cage armor)
-Does the magic effect how the average person lives their daily life?
-Does the magic centralize economic power or disperse economic power?
-Same as above but for politics
-What can a person do to deal with each of these magical powers?
-If the answer is nothing, why haven't the mages taken over the world?
-If they have, what problems might they face?
-Does your magic self-correct, or will you get into detail about it? Say magic shapes the ground and warps a river away from somewhere that needs it, what happens?
-With the magic in mind, does whatever non-magic basis you used as a foundation for your world make sense? (Ex. We all, almost subconsciously rely on what we know to inform us of what we're making. So let's say you started your story with a vague Roman aesthetic. But, if everyone can throw giant unblockable fireballs, marching into battle in a formation would be suicide, so no one would do it. So how do you think an army would form to deal with these giant, unblockable fireballs? Maybe smaller, more stealth focused so they get their fireballs shot out faster? Use your imagination)
Any more questions, just ask. I will reply. Hopefully quicker than this time.