Axe is a popular initiator whose popularity is based largely on his play-style, which necessitates close ranged combat and provoking enemies into attacking him before finishing them off with one of the most satisfying death blows in the game.
Skills
Berserker's Call is usually skilled second but maxed last.
Battle Hunger is usually skilled last but maxed second.
Counter Helix is always skilled first and often maxed first too.
Culling Blade is always skilled (levels 6, 11 and 16).
Items
Starting Items: 2x Tangos, 2x Iron Branches, Stout Shield.
Early Game: Tranquil Boots, Magic Wand.
Core Items: Blink Dagger and Vanguard (OR Arcane Boots, Mekanism, Blink Dagger).
Luxury Items: Aghanim's Scepter, Crimson Guard, Heart of Tarrasque, Heaven's Halberd, Assault Cuirass, Shiva's Guard, Blade Mail.
Situational Items: Arcane Boots & Mekanism (alternative core), Pipe of Insight, Boots of Travel, Vladmir's Offering.