Cho'Gath is very powerful solo top champion. It's abilities gives you chance to deal very strong magic demage and got a lot of HP. Cho'Gath is useful AP than Tank, because he also get tanky and deal a lot of demage ( basicly from Rupture ). In team fight he is very useful, because of his Rupture and his silence.

His spells costs a lot of mana so it is good to ask your jungler to let his blue buffs to you, or to go and try to take their blue buffs. ( Before buying Rod of Ages )

Boots:
1. Buying Ninja Tabi is a good reason if the opponent team has got more AD champions than AP because the static 10% demage reduction which means too much in late game.
2. If you are playing against team with more magic demage wise decision will be getting Mercury's Treads. They are pretty useful against a team which got a lot of stunning / slowing champions.
3. Maybe the best way will be getting Sorcerer's Shoes. They gives you enough magic penetration which is good against tanky team and will be best decision if you go full AP.

Rod of Ages is good starting item because it gives you HP, Mana and AP enough for early game. Because of its passive upon leveling up you will restore HP and Mana, it also gives both of them per minute so best time to buy it is before 15 minute.

Buying Zhonya's Hourglass for second item is nice idea against champions which deal psychical demage, because of the armor it gives. This item is really strong for each AP carry because of the AP it gives and its active, which in team fight and when you get ganked is really useful.

If there is need to get tanky it will be good if you get Rylai's Crystal Scepter. Its passive is really good in team fights and it also stacks with Deathfire Grasp's active.

The only item which you must have on 100% if you go AP is Rabadon's Deathcap.

In late game its good to buy any potions which gives you AP and AD, but only if you are full build.

For Enchantment the best is Homeguard.

Getting 22-3-5 masteries gives you the chance to hold your lane as maximum as you can without recalling, because the HP and Mana regen they give. These masteries also give you enough AP for early game and a bit CDR.

Runes are like the masteries, they gives you nice amount of AP, Mana regen and Magic Pen.

*Getting Mana regen Runes and Masteries is very important for champion like Cho'Gath, because of the mana cost of his spells he got.

Getting Ignite will be really good if you wanna own and push your lane in early game.

For second spell there are 2 variants:

Flash is maybe the most popular spell, and it will be nice.

Other way is getting Teleport. With that spell you can always be on your lane and to be able to gank to other lanes without loosing a lot of XP and time.

Farming with Cho'Gath is really easy. You can justly use his Rupture to keep your opponent far from the minions or just to take them with it. If you don't succeed getting them with Rupture you can finish them with Feral Scream or even with basic attack (with active Vorpal Spikes.

One of the biggest questions around Cho'Gath's abilities is which to max Rupture or Feral Scream.

Pluses of maxing Rupture:
Deals more demage.
Cost less mana.
Have shorter CD.
Gains more % of AP.

Pluses of maxing Feral Scream:
The enemy get silenced for more time.
When the enemy is silenced he can't use his abilities or summoner spells so you can easy catch the enemy with Rupture.