Shen is viable top, supp, and jungle.
For jungle Shen, start with
.
Because of his AS steroid, jungle Shen pretty much goes straight tank.
Your tier 2 boots and smite will depend on the enemy team comp more than anything else.
Obviously jungle item, boots, cinderhulk, tier 2 boots is the normal way to go.
Universal core item for peel and engage tanks like Shen. I normally grab
first over
since the added health benefits him more in the early game jungle than the armor does. Almost always built first unless then enemy team is overloaded on AP.
Useless if you grab Cinderhulk as they have the same passive
vs
Pre-rework (when Shen had lifesteal built in) you'd build SV, nowadays since he doesn't have lifesteal but does have an AOE dodge, Banshee's is more prevalent if you'll be getting CDR from another source or the enemy team has a lot of poke. It is viable to still grab both if needed.
The biggest benefit of SV on Shen now is if you constantly have red buff, an ocean drake, and plan on buying
, then the increased healing adds up to almost Garen levels of health regen.
Enemy abilities can still hit you and allies in your dodge zone
Randuin's was, is, and will always be core on Shen and is usually built second or third item depending on if you need armor or MR first. If the enemy ADC is pulling ahead or you find yourself bot lane more than you're comfortable with grab this in lieu of
as first item. If you're building Cinderhulk, forego
completely.
vs
Deadman's was a great overall core item for him until the recent hit it took which generally leads to Thornmail eeking out slightly ahead in the benefits department. So this comparision is really down to if you need more armor or health.
vs
vs
Offensive itemization is really more of preference now on Shen. Usually
or
and stacking health is all you need cause Shen can stick and initiate counterganks like no one's business.
Moral of the story, health till you're bleeding HP out of your ears. Shen's innate stickiness and ability to answer ganks with a hard shield and tp to the target is his greatest asset, so you need to build around surviving the fight once you get there.
Ultimately, what you build and in what order is highly dependent on the enemy team, but the rule of thumb is health unless you need to build hard armor.
Edit: Forgot about immolate passive, added clarification for overlap of Cinderhulk and Sunfire.