As a top laner it's important to include multiple Health potions as well as a Sight Ward to your starting item's to keep you healthy in lane and safe from ganks. Rejuvenation Bead is a part of your Warmog's Armor, but you can replace it with more Health potions or a second Sight Ward as a safer route.
Doran's Shield is an amazing item to get on your first back for Shen to shutdown any haras from physical damage dealing top laners. Buying it will delay getting your core item's, but on the other hand it lets you farm more safely and sustain in lane longer making it a worthy purchase most of the time. Don't buy it versus mages like Rumble or Vladimir, start working on your Warmog's Armor when laning against them.
Sunfire Cape is the perfect item for Shen. It gives damage, tankiness and splitpushing power all in one. Don't underestimate the damage from the burn effect of the cape especially if you buy Sunfire before Warmogs, forcing trades with your Shadow Dash allows you to melt the Health bar of the opposing laner. Sunfire cape is a very snowbally top lane item in general because for any Physical damage dealing bruiser it's extremely hard to trade damage with someone who has a Sunfire Cape. If you are laning versus a magic damage dealing champion such as Rumble or Vladimir, buy Warmogs first and Sunfire after it.
Warmog's Armor makes Shen an immovable object. 1000 Bonus health coupled with the Health regen of the item, sustain from Shen's Vorpal Blade, the spammable shield Feint and defensive Runes and Masteries simply means that once you get it it's hard to die to anything. You can stay in lane forever, dive turrets and tank multiple enemy champions in teamfights and skirmishes.
Ionian Boots, Ninja Tabi or Mercury's Treads
All three of them are very strong choices. Ninja Tabi's are very strong for laning phase if you are playing versus an Auto attacker like Xin Zhao, Ionian Boots help you reach that 40% CDR cap more easily which is very vital for Shen and Mercury's Treads are expensive, but a good source of Magic Resistance and Tenacity. If Mercs are the boots of your choice, don't rush them but rather leave them as Boots of Speed until you finish your core items.
Late game items
Cooldown reduction is a very strong stat on Shen to get more Taunts and more shields off in a teamfight as well as having Stand United available as often as possible, leaving you the ability to splitpush. Aim to get around 30-40% Cooldown reduction every game with a combination of items of your choice.
Locket of the Iron Solari
Locket is a strong item to have in teamfights and even without the active it gives a moderate amount of Health and Armor for only 2000 Gold.
Shurelya's is an extremely strong mid/late game utility item to have in a team, but it doesn't give great stats for the owner of it, only a moderate amount of Health and very little Regen on top of the 10% CDR which is the main reason why it's a strong item for Shen. Get Shurelya's either if your team is ahead and you want to force engages, or if your team lacks counter-initiation. Remember that there's nothing wrong in having multiple Reveries in a team unlike Aegis for example, the more the better.
Spirit Visage is an excellent Magic Resistance/Cooldown reduction item to mitigate the damage you take from mages. It's an excellent item for Shen in most games, but if the enemy team does not have any magic damage dealers, don't buy it. The 20% Healing increasing passive does not work with heals from other sources than Shen himself, such as allied Soraka heals for example.
Randuins is an excellent late game item for Shen as you will be usually getting focused by the enemy AD Carry in teamfights because AD Carries must attack the frontline only to maintain their safe position. The active is also very strong if your team lacks assasination strength to finish the low HP enemies in teamfights since you can use the slow to make sure that nobody escapes from your team.
Statikk is a cheap item which mainly increases your splitpushing speed and Movement speed, but it does slightly increase your damage output in teamfights as well. I recommend including either Statikk Shiv or Wits End in your build most of the games.
Wits End is similar to Statikk Shiv, the differences mainly being that Wits End is slightly cheaper, gives more single target damage and gives a decent chunk of Magic Resistance, while Statikk Shiv is a bit more expensive, clears minion waves faster and gives Movement speed. It's an excellent damage and Magic Resistance item for Shen overall, but if you aren't tanky enough in teamfights then Mercury's Treads, Runic Bulwark and Spirit Visage are better Magic Resistance options than Wits end.
Mallet is a solid pickup when your team lacks Crowd control or when you need to be able to peel for your carries better.
Aegis of the Legion / Runic Bulwark
Aegis of the Legion is a very cost effective item when you add the stats your teammates get from the Aura. Every team should usually have at least one Aegis or Bulwark, but it's almost always either the jungler or the support who buys it because they don't need to buy big selfish items first, like Shen needs his Sunfire and Warmogs. If late game no one from your team has it, buy it.
Never get this item on Shen. Shen has AP ratios left in his kit because years ago he was more of an AP Tank, but he has gone through a lot of changes since then. If the item would give a lot less AP and more Magic Resistance it might be a decent item for Shen, but it's just too AP heavy item for Shen right now.
TriForce Shen is largely popularized by Darien of Gambit Gaming who has been doing it from his EUNE/Empire days to present. It's a very different build from rushing Warmogs and Sunfire and a uniqueue way of playing Shen. Triforce is very expensive and only gives a little bit of tankiness through the Health the Phage gives. Feel free to give Triforce Shen a try in a normal game and see what you think, but personally I don't like it or wouldn't recommend anyone other than Darien to do it in a more important game.