I picked these Summoner spells because I find that Cho' Gath does tons of damage, but its burst so the extra ignite helps him, early game. Flash for the feast combo and as well to get out of tough situations.

With all these Ability Power items, you can dominate the opposing teams carries. By Rupturing them then flash feasting, therefore making the opposing panic and run. With hourglass you can be up close and personal, activate it and save a couple seconds in the team fight. So it benefits, you and your team. With Abyssal Scepter it reduces all the nearby enemies Magic Resist which helps your team as well as your AoE abilities, AND give your Magic Resistance, its just an overall amazing item to have.

As an AP Cho'Gath I would recommend last hitting Creeps, because of Cho'Gaths passive, you will be able to harass whom ever you're laning against. Not only that but it also helps you get your Quick Massive Ability Power Items. Which then makes Cho'Gath unstoppable.

So as cho'gath you should always focus the opposing teams carries, so i would make sure my Rupture would hit the ranged first and when they're low my carries will pick them off for the sure kill, then i would feast their melee damage dealers(for example: Xin Zhao, Jax, Pantheon) because of all the Crowd Control they have.from AoE damage, to AoE stuns to pantheons solo stun, I don't want them to hit my carries at all.