Academy is probably the best for that, under the conditions you state. Back when
Urza's Saga came out, that was probably the best deck ever. (the B.S. with 4 windfall, 4 time spiral, 4 tolarian academy etc etc) I'll never forget reading this guy's description of a 10 round goldfish test right after Saga came out: 6 1st turn kills, 2 2nd turn kills, 1 4th turn kill, and one loss for stroke of geniusing himself for too much!

Anyone can make a deck that wins 99% of the time on turn 1 if they ignore the restricted list (endgame shandalar decks are proof of that!) so here's some that work to varying degrees if you follow the type 1 rules:
Other ideas that can kill on the first turn:
-
Goblin Charbelcher deck. The idea is to have lots of mana sources and very very few lands, as well as 4
Land Grant.
-
Hatred deck. This one isn't so reliable, but you can make it happen
-Channelball deck.
Channel's restricted, but with a dream hand you can win first turn
-
Sneak Attack deck. Again, you'll need a dream hand, but something like land, 2x mox, mana vault, sneak attack, serra avatar is game.
-Elf deck. (yes, really) With the right draw, you can make enough mana to do anything you want, and then win with
Fireball or something like
Akroma's Memorial to give thirty elves haste or whatever
-Ad Nauseum deck. Basically, use ad nauseum to draw your whole deck, and design it so that all the cards have very low casting cost, and then kill with something like
Tendrils of Agony-
Archive Trap. It's a one in a billion shot, but if opponent goes fetchland, go, and you have four archive traps in hand, it's game over :p
-Kobold clamp deck. It's not very reliable, but it can work.
Skullclamp your 0/1 kobolds, use stuff like
Glimpse of Nature or
Carnival of Souls or
Cloudstone Curio, and some kill like
Tendrils of Agony-
Dredge deck. It's probably not very likely to win on turn one, but if things work out, it could. It is very consistent at winning by turn 4 or 5 though
-
Dragonstorm. It's not very reliable either, but it could win on turn one as well.
-
Eureka +
Black Lotus and whatever dream hand you can come up with
-haste creatures and
Berserk, again with a dream hand something like land lotus mox ball lightning 2x berserk is possible
-anything that can get
Time Vault and
Voltaic Key out and untap the vault on turn 1, such as those two plus
Mishra's Workshop + Mox
This isn't a deck, but to build first turn kill hands, you'll want to pay special attention to the following:
-most cards on the restricted list (most are there for a reason!) Especially the Power Nine,
Fastbond,
Yawgmoth's Will,
Tinker,
Demonic Tutor,
Wheel of Fortune -zero mana artifacts, especially mana producing ones like
Chrome Mox,
Mox Diamond, and the restricted ones
-anything that draws cards, especially for low mana cost (like
Ancestral Recall,
Wheel of Fortune,
Windfall,
Infernal Contract,
Frantic Search)
-anything that makes extra mana, like
Dark Ritual, moxes,
Mana Crypt,
Lotus Petal,
Elvish Spirit Guide,
Simian Spirit Guide, etc
-storm cards
-anything with pay
X life: do something, like
Hatred,
Yawgmoth's Bargain,
Channel-anything with an alternate casting cost, like
Gush,
Dread Return, etc, or that lets you cheat stuff into play, like
Eureka,
Show and Tell,
Sneak Attack,
Shallow Grave (and other reanimation, but that one's nice for turn 1 kills because it gives haste)
-lands that produce more than one mana and do not enter play tapped, such as
Mishra's Workshop,
Gaea's Cradle,
Ancient Tomb, etc
-anything that tutors for cards, especially at low mana cost, and especially that puts it straight into your hand, like
Demonic Tutor or
Grim Tutor, or straight into play, like
Tinker-miscellaneous completely broken stuff like
Mind Over Matter or
Skullclamp, as well as anything I forgot to put on the list that should be here :p
Probably the most reliable ones are going to be academy, tendrils, ad nauseum (though I haven't tried that one yet), and belcher.