The most important and the first of the list is Feast. I've seen many players neglect feast and it can be the deciding factor between a win and a loss. Feast should be saved for champions, dragon, and Rift Herald/Baron. These give you unlimited stacks. Too many people immediately attack minions to build the "free 6" stacks. These hurt you because early game Feast is devastating to nearly all champions. If you can save it and devour champions it will help you get much stronger in the late game.

This is very situational. Depending on the opponent as well as the CS coming in I either go for Hextech Revolver or Lost Chapter. If I'm ahead on CS and the opponent has a movement speed equal or only slightly higher than mine I build the lost chapter. The Lost Chapter eventually will build into Archangels Staff which gives you a ton of AP as well as some much-needed mana. If the opponent is significantly faster than Cho I build Hextech revolver and build into Hextech GLP-800. This gives you an active spray of icy bolts that will slow them. Slowing them will help you use your ult to feast. or to effectively hit Rupture.

These are the four most important items for Cho'Gath. The first three focus on his AP. The Warmog's Armor gives you insane health as well as the passive Warmog's Heart. This gives you 5% max health restore per second once you are over 3k health.

These items are very good items but tend to not be as effective for Cho. If you have a significant CS lead then I would recommend saving for Rabadon's Deathcap, but without the huge lead, the cost can sometimes hurt you in the long run.