Over the course of her life, Ororo Monroe has been trained as a juvenile thief, worshiped as a goddess, and hated as a mutant. Since Charles Xavier enlisted her to join the X-Men, Storm has grown as a warrior and as a leader.Marvel Source
Her control over the climate has been honed through constant training and numerous battles, and her arsenal of elemental powers, from shattering lightning strikes to freezing winds, make her a force of nature to be feared and respected.
Since 2.1, Lightning Storm has become one of Storm's most powerful attacks, so this will be your primary AoE attack, paired with Crashing Hail (and Lightning Column for harder trash that is more difficult to kill).
When fighting bosses, alternate between Lightning Column and Stunning Bolt for lots of damage as well as a much higher chance to stun, and periodically apply Crashing Hail for extra DPS and slow.
Use Sirocco Rush or Windy Flight to move around more quickly as needed, such as when dodging attacks or traveling long distance.
Gusting Tempest and Crashing Hail are meant to be used to apply Turbulent Winds, which is probably one of Storm's most helpful passive abilities. When these three are combined with lightning attacks like Lightning Storm or Lighting Column/Stunning Bolt, you should be able to kill bosses and large groups of trash with complete ease.
Artifacts and the Madame Hydra Medallion are primarily meant to boost DPS, Amulet of Agamotto helps when trying to recover from heavy attacks. Plus, it boosts attack speed, which is extremely beneficial when fighting bosses with your basic attacks. The invulnerability provided by the medallion and Watoomb can be helpful when fighting bosses or trash with high DPS, and the healing provided by Relic of Lemuria and by the costume core is great for survivability.
In terms of gear, focus on damage rating and defense for extra DPS and survivability, respectively.
This build does leave you a little squishy, but if you are paying attention while playing and know how to handle certain situations you will have a very little chance of dying. It's not as easy as some of the Thundering Maelstrom leveling builds out there, but it is very efficient.
Spirit should not be a problem if you use Lightning Storm/Crashing Hail in moderation with Lightning Column/Stunning Bolt. But, if you do need spirit and/or if you're losing health, the costume core should provide instant spirit, health, and invulnerability when you use a medkit so that you can last a little longer.