Warmog, you need to get KILLS, I mean KILLING enemy champions. You NEED to get fed to get Warmog early. Early enough to make it useful. I am serious.
Shen is not that good at farming minions. His only damaging skill is Q and Auto Attack. You cannot farm that well. I played quite a few games with Shen. I never ever get more than 100 or so minion kills. I typically get around 70-80, I'm usually getting assists and tanking.
So no Warmog because even if you get fed early game, you won't be able to fully get all the stacks.
This is generally my build.
Being harrassed a lot (low gold income) - Heart of Gold
Boots +2 (Ninja Tabi, Mercury's Treads
Physical Heavy - Warden's Mail/Randuin's Omen, Sunfire Cape
Magical Heavy - Banshee, Force of Nature, finish Randuin's Omen later (good for tanking tower and Active)
Mix - Get Negatron Cloak, Finish Randuin's Omen, Banshee, Force of Nature, Sunfire Cape
Able to hold the lane/push them back - Parts for Aegis of Legion
Finish Aegis of Legion/Finish Boots (depends if you need to chase or walk a lot)
Finish Frozen Mallet
Normally, if I can get Aegis, I like to go for some offense (Frozen Mallet). I can dash/taunt. Sometimes I use it to chase even if I cant get in range for taunt. But I can slow them with melee. So it still works out in the end. I get the Guardian Angel, for a mix of Armor and Magic Resist. I don't really rely on the revive.
Bottom line, pick items that give you tankiness (armor/magic resist) that also gives HEALTH.