Cheap, aggressive creatures with loooooooots of bolts. We run eight wizards, so it's not hard to turn on Wizard's Lightning, and when it's not live you can just discard it without remorse. Fiery Temper is a live discard, and Lightning Bolt is always good. Lightning Axe is more removal and a cheap discard outlet. Our creatures are cheap and aggressive, and our vampires give us some long game. Bloodhall Priest gives us reach, an etb removal effect, and gives us synergy with Soul-Scar Mage to shrink big threats. Our utility lands give us reach and removal in a pinch. Oblivion Crown is a fine madness outlet that also lets us pull combat tricks, especially with Flameblade Adept. With a Asylum Visitor out, you can even pseudo-cycle on your opponent's (or, more likely, your own) upkeep to dig for answers. We discard enough and have enough cheap spells that Bedlam Reveler comes online fairly fast, refills our hand, and is itself a discard outlet.

Alms of the Vein is probably the only non-self explanatory sideboard card; it's there as a Bump in the Night with lifegain attached to give us an edge against other aggro decks.

Note: a Grixis build is probably objectively stronger, as it ups the number of wizards you run effectively (hint: Stormchaser Mage, Snapcaster Mage or Adeliz, the Cinder Wind) and gives you access to Thought Scour & Opt, but I didn't feel I could torture the mana base enough to get that build without compromising the budget aspect. You could always just add Crumbling Necropolis & Fetid Pools and add in painlands/checklands to salt, but that would be soooooooooooooooo slow. You'd probably almost be better off just running 4x Crumbling Necropolis, 4x Evolving Wilds and basics. Point is, this deck needs to be fast and losing a turn due to taplands just hurts too much. Canyon Slough gets a pass for cycling and having both land types for Dragonskull Summit, but otherwise you simply cannot start slow with this and have any real chance at winning. A nonbudget version of this deck would for sure be better as Grixis, with fetches/shocks, Snapcasters, and Thought Scours being pretty good upgrades all round. Bedlam Reveler also works better in the Grixis build, as you can more easily fill up your graveyard with the critical mass of instants/sorceries needed. Having counter-magic in the sideboard could also be nice; I feel like Rune Snag could be weirdly good in this deck with the rate it churns through itself.

In the end, this is a weird Sligh deck and plays like it. Go fast, go hard, kill alls the creatures and swing in with your over-performing cheap guys. Have fun!

Edit: I finally ponied up for a pair of Collective Brutality, which, along with a second Bedlam Reveler, have taken the Oblivion Crown slot. I still irrationally love Oblivion Crown, but it's time to call it quits on that experiment :/. This does, however, bring us up to 20 instants/sorceries, which IMO justifies bringing in the second Bedlam Reveler as a finisher. Having played the deck quite a bit since my original write up, I can say it's vitally important to have a finisher in this deck. The abundance of pseudobolts and aggressive creatures makes it easy enough to get your opponent down to the 5-6 range, but by that point the opponent has often stabilized and you get reduced to praying to rip a fiery temper off the top and casting full price (this is also the reason why Ramunap Ruins is so great - uncounterable instant speed damage is very, very nice for closing out the game). Having late game threats mitigates this; even the humble Gurmag Angler gives you a way to close out games, while Bedlam Reveler does the same while digging deeper for burn spells and even providing a madness outlet in a pinch. Bloodhall Priest is also, IMHO, a vastly underrated finisher, especially with a Soul-Scar Mage out on the battlefield. Getting repeatable removal/burn on a strong Madness-able body is very powerful for this deck. Having a 2/2/2 split on the three finishers is what I've arrived at, but I can see an argument for a 3 Angler/3 Bedlam split being better (or even a 4/2 split either way, depending on your instant/sorcery count).

At this point I am eagerly watching the Ravnica spoilers now that Jumpstart was spoiled for the Izzet; if a Lightning Strike equivalent with Jump start is spoiled I might just jump the gun and cut both Bloodrage Brawlers and both Lightning Axes.

EDIT: I finally have a playset of Collective Brutality, so I've included them in the decklist. If you want a budget version of this deck, swap them out for three Bloodrage Brawlers and another Gurmag Angler (or Bedlam Reveler or whatever). You could also go for another Lightning Axe pr two if your meta is big into fatties. Essentially, bring in a discard outlet that either provides a lot of pressure (ie Bloodrage Brawler) or is an answer to one of their threats. Bloodrage Brawler is probably a safer call, but I think Lightning Axe has a higher ceiling and is a slightly better discard outlet, being at instant speed and one mana cheaper.