*For Budget Players -- The expensive part of this deck is the mana base. The Misty Rainforests and Scalding Tarns alone cost $555. The only other expensive cards in the deck are the Blood Moons at $45 per copy ($90 in this deck). None of these cards are essential to the storm strategy, and therefore the storm deck itself can be built for around $200.
Now to the card choices ...
Creatures
Goblin Electromancer -- Effectively makes the rituals produce more mana. It does turn on some removal, but its upsides more than outweigh that, allowing you to greatly increase your storm count.
Spells
Pyromancer Ascension -- The engine of the deck. It basically doubles everything you do. Notable exception is that it does not copy the "storm" part of Grapeshot or Empty the Warrens.
Past in Flames -- Flashback to all spells. Basically flashback your rituals, and then storm for a lot.
Thought Scour -- Great synergy with Pyromancer Ascension and Past in Flames. Also card draw.
Desperate Ravings -- Card Draw. The random discard is largely irrelevant as the deck has so many redundant cards.
Gitaxian Probe -- Free card draw and/or gives you information about whether or not it's safe to combo off that turn.
Serum Visions -- Solid card draw and scry helps set up the combo.
Manamorphose -- Mana Cantrip. Basically a 2-in-1 for the deck.
Pyretic Ritual -- MANA!
Desperate Ritual -- Generates mana to combo. Splicing Desperate Ritual onto Desperate Ritual and then playing the second ritual is also fun.
Grapeshot -- Win condition. Fairly self-explanatory. Noteworthy is the fact that the copies still resolve even if Grapeshot is countered.
Sideboard
Blood Moon -- Wrecks Amulet Bloom, Scapeshift, Tron, many tricolor decks (looking at you Junk), etc.
Empty the Warrens -- Alternate win condition. Sided in for Grapeshot when you expect burn hate. After all, Grapeshot is burn.
Naturalize -- When you expect Rule of Law, Eidolon of Rhetoric or Rest in Peace, as Izzet has no enchantment removal. PLay this off of the Breeding Pool or Manamorphose.
Dispel -- Good for countering spells that may interrupt the combo and adds to the storm count in the process.
Lightning Bolt -- Needs no explanation.