Haha! I had to stop using Chain Lightning because I kept taking Lydia or the dog out.I use Lightning primarily on my Mage since I'm usually teamed with a melee-based follower. Shock spells do not have an AOE, so it doesn't place my follower in danger unless I outright blast them in the back (Lightning Bolt / Thunder Bolt).
Haha! I had to stop using Chain Lightning because I kept taking Lydia or the dog out.
While your points are good and personally I use shock most of the time it is probably best for someone with a battlemage build to use fire or frost because they will have less magicka (unless you are an Altmer or are using some other method to combat this). You will probably want to use a combination of both fire and frost because they are both really useful but you may wish to focus on fire.I'd go with shock; it fires immediately rather than shooting a ball and only one monster is resistant to it. Fire does the most damage and it damages over time, but more monster are resistant to it. Frost is good for slowing down melee enemies, but most monsters are resistant to it.
Fire would be second.