Ive recently played a lot of Urgot, and this is the build that I use.

I tend to lose lane early due to poor waveclear, then come back in teamfights. The long range on the Lock-on Q, and the Armor shred helps secure kills. The armor shred on E + Black Cleaver helps amplify your ADC to the next level, and with skill, you can kite well enough to stay alive.

Stay safe, harass once you get tear. Focus on CS before that.

I tend to get Black Cleaver before Manamune, because of CDR and armor shred, sometimes Glacial Shroud if i get much gold, because the CDR is very helpful, and Manamune is quality, but more worth it when you have high stacks.

Tips; Q when you are walking to lane to get more stacks on tear.
In lane, try to freeze it if you can. Farm under tower if you have to. Urgot is very susceptible to ganks, as he has no real escape, and his ultimate usually puts him in a worse position.

Don’t ultimate early in a team fight, this will put you in the middle of their team. Wait until you have some of the threats down, then use the damage reduction to your advantage as you pick off the last few enemies.

Alt items; Frozen Heart over Iceborn Gauntlet if against a top lane ADC like quinn or Atk speed based jungle.

Guardian Angel if for some reason you get focused and dropped quick.

Youmuu's Ghostblade if you are against an all AD comp, with little real magic damage.

Mortal Reminder if the enemy team is stacking bonus armor. It does nothing if they do not have bonus armor, unless they have high lifesteal/regen champs.

Mercurial Scimitar This can be useful if you get CC'd down hard.
You can take gage if you are facing much burst with little front line, but i wouldn't think it's that great.

Cull Urgot is a farm heavy champ, if you feel like you are good at CS, this can be a decent buy. It is popular among pro ADC, but it takes up a valuable spot in your inventory, especially if you are slow to get the 100 CS. I would buy this after tear, because having mana to Q is very helpful for CS.

Rune are standard late game bruiser. Alternative; take one or two scaling mana regen blue, take 3 AD quint or one more AS quint.

VS Champs. Urgot is strong vs champs that don't build defense items due to long range poke, urgot is ok against bruisers but can easily be bullied, vs pure tanks urgot can do ok, but has less kill threat.