I go
first, everytime. He needs it for waveclear, and dueling power.
After that, there are five offensive items you can choose from:

Suffers from an awful build path, so I would only buy it if you have someone on your team who can benefit from the shred, and you can build it all in one go. Riot said they plan to change the buildpath, so this may change.
This item is probably you're best bet in most situations. If you get this, then go full tank, you become an amazing duelist. However, if there are no tanks on the enemy team, there are better options.
and
This is a very offensive combo, can can work wonders if you are ahead. It gives you the power to actually assassinate carries if you can taunt them. You'll actually feel like a ninja! Be very careful with this, you need to be A: Ahead, and B: Have alot of cc / another tank on your team who can peel. Shen's job is usually to peel, this build puts you in the role of an initiator. This also gives you great splitpushing power.
This item without shiv can be very strong, but overall is outclassed by bork. Can be a good solo pick up if against squishy targets. Keep in mind trinity will give you 100 extra on your ult.
I have never built this on shen myself, as I do not feel it is better than any of the items listed above. However, it is popular on him, so it might be worth buying. It gives good split pushing potential, and more AoE damage, but shen doesn't do much damage without different items listed above... Be careful with this one.
Keep in mind that you are still a tank. The trinity/Shiv combo is the only exception to the "Only get one offensive item" rule.
Always build
or
(Against AP's) first. After that, pick up your offensive item (If you are not really far behind), and then tank up.
Flat HP gives shen very good heals for his team on his Q, and more damage for his passive.
is also excellent.
This is for toplane shen, if you are in the jungle, get CinderHulk, and go full tank.
, Cinderhulk, and smite gromp. That gives you more than enough damage, believe me.