I've seen several Storm guides, but after playing a while I've developed my own style that's quite different from the guides, so here is what I've found works well from my experience. This is for PvE only.
Firstly I'll say that I love Storm, it's my favorite school, though I haven't played Life or Ice. Storm levels the fastest because you can quest the fastest with Storm.
Secondly, my style of Storm is to go full out offense all the time. So:
Secondary spells: 1) Ice to Tower Shield 2) Elemental Blade 3) Reshuffle 4) Blood Bat (I'll explain later) 5) Sun, Moon and Star stuff
Forget about Life. Many people say to take Life to Satyr, but this is a waste IMO. I found myself never casting life and if you are casting Satyr you're already in big trouble. You could also take Death to Feint, but...
As soon as you can, start farming Stinkweed for Feint Treasure Cards. I found that I was able to get enough Feint treasure cards that I never really needed to train Death. For me, I only use Feint in very hard fights and with farming large plots of Sinktweed I always have plenty.
Also farm Honey Sickle for Balance Blade and Storm Blade treasure cards.
For gear, focus on +Accuracy above all else until you get into the +20% accuracy range, then you can start taking other things into consideration. Buy new gear at the Bazaar every 5 levels once you get to level 10.
Other gear to focus on: Get the Storm Trap Amulet ASAP: Sokkwi's Necklace of Skies (level 15)
For wands you want to either be using a Myth wand or a Storm wand. If you get a really good Storm wand, like the one from Zeus or something, then use that and put Blood Bat into your deck. Otherwise use a Myth wand.
You want to have easy ways to remove Myth and Storm shields and to get rid of Weakness, etc. For this I prefer using a Myth wand, which lets you get rid of Weakness and also remove Myth shields when you are using Prisms. But if you use a Storm wand, then put Blood Bat into your deck for the same purpose. Earthquake treasure cards can also be useful situationally.
When using a Myth wand I keep 3 copies of Thunder Snake loaded just in case I need to remove some Storm shields. This is still hassle and may use up any blades you stacked, but it is good to have as an option. Another option is to stack a prism on top of their shield to just get around it.
Once you get Tempest that will be your go to spell for quite a while. I typically run Tempest and Thunder Snake, with Myth wands as my basic attacks for general questing. For dungeons it's dependent on the type of boss you are facing and your group.
I found that I was able to start soloing the Temple of Harmony by level 30 using this type of setup.
The key to this is to build up your Blades and Traps as fast as possible and hit hard before they get a chance to do much harm.
I don't have good advice for pets. I had a hard time farming for pets, but finally got a Cloud Colossus as my first.
