Currently I'm only level 13, playing as a caster, but I'll give you my experiences so far:
Having never played a caster before, I'm not sure what the best route to go is, but currently I'm going heavy into destruction tree (the elemental damage one). It's fairly weak to be honest, but it's also mindless. I just double-hand the flame spell and burn the enemies away. Some mobs are resistant to fire so in those instances I switch to the ice or shock spell equivalent.
On the skill tree you can, of course, increase the amount of damage done for each element, but it's slow going. There are 2 levels to each, but the first one you can get at skill level 20, but you won't be able to get the second one until skill level 60, which is a ways off. So for a long time you feel underpowered.
Killing small mobs are no big deal using this strategy, but boss mobs and larger mobs (like giants and dragons) become problematic, because they can basically one-shot you. I am wearing cloth at the moment for the mana regen and mana perks, obviously I would prefer to have light armor with the same stats but at this early level they are not readily available and I do not have the crafting ability to make them yet.
To deal with bigger mobs, it's important to have a companion or NPC to "tank" for you. Now, it becomes kind of a pain because your companion will get in the way of your spells, but they can't really die....if they go to zero health they just take a knee until they regenerate. So on boss mobs I find it best to have them tank and I just blast away with spells. If my companion goes down, then I summon an archon using the conjuration tree to tank for me.
One interesting thing I notice is that I burn through a ton of potions. I'm drinking health and mana potions a lot more than I ever recall. My original playthrough many years ago my character was so tough I don't think I ever had to drink potions.....maybe stamina just to keep DPS up, but seldom health potions and never mana potions. So this time there is a little more strategy in that I have to have many potions ready to consume, which means I do use alchemy far more than I used to.
I'm still sneaking around and pickpocketing, to raise those skills. I've been toying around with the idea of sneaking around and using fear/charm/confusion spells, which I might try out once I get to Winterhold and get going on the mage quests.