AP is the more viable and the more common but AD/tank sion completely rolls face late game
he gets so farmed, has so much health, does so much damage, and heals his entire team
Sapphire Crystal
Sheen
Berserker's Greaves/Mercury's Treads/Boots of Mobility
Infinity Edge
Warmog's Armor
Atma's Impaler
Sheen is non-core, you can actually sell it if you want to. Alternatively you can build Trinity Force out of it, but it's not mandatory.
You should never build straight AD, but rather crit/tank just because his Enrage gives him passive AD and the health gain is great with Atma's Impaler. Core on him would be:
I-Edge, Warmog's, Atma's, Boots
Good finishing items are:
-Youmuu's Ghostblade (Armor pen, crit chance, AS, speed)
-Phantom Dancer (Speed, crit chance, AS)
-Trinity Force (Speed, crit chance, on-hit procs, slow, beefiness)
I would say go the Ghostblade just because of how fast and powerful it makes you, as the ArP really helps.
Defensive items include:
-Force of Nature
-Banshee's Veil
-Sunfire Cape
-Randuin's Omen