I'm not the best shen, but I would think HP/def and AS are your priorities. The HP helps your def plus the extra damage from your passive. And the AS helps you get your passive off more.
With that in mind, Witts end, and overlords bloodmail are probably priorities, and you'll want either ninja tabi or merc treads depending on other team. From there you could build more defense or more damage depending on how you're doing.
If you're not super familiar with TT, the one thing you have to be careful of with tanks is not building TOO tanky. You can't build full tank on TT, because then the other team will completely ignore you and your team will lack damage. The goal is to stay in a sweet spot of as much damage as you can build while still surviving on the front line, which of course takes a good bit of defensive items, just not all defense.
I feel like defensive items are pretty straightforward to choose from here, just prioritize ones with HP also as it helps your damage through your passive and build against who is doing most damage on the other team. So aegis and sunfire cape can work well.
For damage, I think trinity would work well if you are doing well enough to build it. build sheen or zeal first depending on your preference and only finish if you are doing well. Plus zeal gives extra MS which helps a lot for split pushes.
On that note, you should try to split push when you can pull it off, especially if you are ahead as you can force towers then ult to your team when needed. If they all defend vs your other 2 pushing, you can hit the tower in your lane, and if they send 1 to defend vs you, you can ult in for your team to dive.
Lastly, in teamfights, you'll be tempted to taunt right away, but try to save it at least a moment or so for a good opportunity. Either, when someone jumps on your carry, or when their carry is positioned to do a lot of dmg, or if you can get 2-3 of them.
Like I said, I'm not an expert and maybe people will have better ideas, but hopefully this helps!