Minecraft wiki entry for Things_not_to_do, associated text: Armor (Full Iron or better)
A good sword (Iron or better)
Pickaxe (Stone or better. Stone pickaxes can only mine iron, lapis lazuli, and coal. The player needs an iron pickaxe or better to mine any of the other ores, and diamond to mine obsidian.)
Optional bow and arrows, but recommended for killing skeletons, creepers, and witches.
At least one stack of dirt or cobblestone (The player should remember to dig up more along the way.)
Water bucket
Food
Torches
Compass and/or map (if the player plans to just explore)
Bed
Crafting table (this comes in handy, especially at night)
Fishing rod (in case the player runs out of food).
Wood (useful for crafting while the player is away from home)