Is there any real advantage to using one over the other or does it just depend on the enemy your attacking.

Fire does some dot damage as well, frost slows and drains stamina, and lightning strikes the target instantly at range.

Fire dragons, atronachs etc, dont use fire. Frost dragons, atronachs, use fire. Or use lightning for either.

Note-to-self: read the body before posting.

Any way all the elements have their advantages, Fire>Frost>Shock and vice-versa.

Also note:
Fire does extra health damage
Frost does bonus Stamina damage
Shock does bonus Magicka damage

So you might want to consider mixing it up like having Frost and Fire damage on a target so they die before they reach you.

Lightning also damages the target's magicka, so is useful against mages.

actually wouldnt it be a better idea to go with focusing 2 types instead of just one due to resistances(when they get fixed) that way you're not entirely screwed when it comes to fighting things that are resistant to your 1 element you decided to focus

So i really should increase all three , cool.

yea why not, gives you a bigger damage variety in elemental stuff compared to melee ppl

well.. the adept spells have different effects. chain lightning is rather crap but ice storm and fireball are decent (i liked ice storm the best so i went with ice)

fireballs seems to be the loser of the three, at least to me. Chain lightning can be arched around corners and ice storm goes through walls.

different element uses different amounts of magicka.

fire is least, frost in the middle, shock takes the most magicka.

however a important factor is that lighting spells are instant. it goes where you point it. instantly.
spells like fire ball and icy spear are obviously projectiles and wont always guarantee a hit.

and theres also the extra damage, drain stamana and drain magicka for each element.