Winning a 3 Rune game

Winning a 3 rune (basic) game is often a tough idea for new players, who are swamped with trying to learn the controls and various enemies they need to defeat. This article should serve as a resource that will provide a framework to follow.

The order of winning
The general order for winning a game goes something like this:
 * Dungeon until Lair
 * Lair
 * Dungeon until 15 or Orc (can switch between the two to taste)
 * Return to Lair. Complete either Swamp, Shoals, Spider or Snake. Which one you do is based on preference, resistances, build and equipment. Each branch will be covered in depth later.
 * Complete the other option in the above step. This puts you at 2 runes.
 * Go to Vaults, down to V:4. Do not touch V:5!
 * Go to Depths.
 * You now have a choice between Slime, Abyss and Vaults:5. If you survive this step, congratulations.
 * Zot 1-4
 * Zot 5. I put this in a different step because you should treat it like a "boss floor".
 * Orb run

At some point after depths, you can choose to go to Crypt and/or Elf, keeping in mind that the mere act of entering the place increases your chance of dying by 10% (not literally, but just don't do it unless you're 100% certain to die without more stuff).

Lair Branch Checklist
Here's some stuff to help you figure out which branch is the right one for you to go to. They are listed in order of importance.

Swamp

 * Something to fight against Hydras. Spells, blunt weapons or flaming edged ones.
 * rPois
 * Flight
 * Some way of dealing with a Thorn Hunter

Spider

 * Good positioning
 * rPois
 * Clarity
 * Something to kill Scorpions
 * Sinv and/or Invisibility

Snake

 * Very good Combat ability
 * rPois

Shoals

 * Flight
 * Repel Missiles
 * Invisibility (trivialises this whole branch if spammable)
 * Magic resist
 * Healing (These guys HURT)

Generally, you can expect fast, light attacks with poison in Spider, slow heavy attacks in Snake, mixed attacks in Swamp and fast, heavy attacks in Shoals.

Vaults
Vaults is a somewhat more difficult version of the dungeon. You will rarely die there until you meet the Vault guards: Ironbrands (Red), Convokers (Yellow) and Sentinels (Blue). Being marked by a Blue guard, having doors closed on you by the Reds and being heavily swarmed by the Yellow's summoning are all instantly dangerous. Yellows are countered by killing them very quickly, Reds are countered by isolation and Blues are just straight annoying: Run to the exit or a corner and be ready to burn consumables if things get too tight.

Vaults 5 can be difficult for a 3 rune game because of these guards. Having a blue one mark you in V:5 is often a death sentence without cancellation. There is almost no feasible way to fight through an entire alarm period with a mediocre character. You will need to burn multiple teleports and pray to whoever you're worshipping that you get out of it losing just a few potions. The Red guard, or more accurately the threat of them existing makes it extremely risky to stairdance the initial ring of vanilla guards. In addition to this, you will see the regular Quicksilver Dragons (which remove buffs on breath weapon, including teleports), Titans (smiting and lightning bolts) and the odd (Ancient) Lich.