Well, this is my first guide, so it might be pretty weird. Anyways, I love cho'gath and I play this character quite a lot. I have had a lot of experience with this character, but i play him quite unusually. I build cho'gath as a offtank dps on-hit character. This means that I play the character as a tank, but don't make him as tanky as i can, but make him quite tanky nonetheless. Hope you enjoy reading my playing style. :)

I chose these runes obviously for the attack speed. I do not actually use the quintessence of alacrity, but the greater quintessence of endurance works quite well as well (increasing max health by 1.5%). The attack speed is very useful as my build of cho'gath, like many dps' characters, need quite high attack speed.

Cho'gath is usually a tanky character as many people build him to be a tank. But as this build lacks in the defensive abilities, I decided to have defensive masteries and put the rest on offensive masteries (as this build is for dps). I just think the higher tier masteries are more useful in general, such as juggernaut.

I usually start off with boots then ninja tabi, but sometimes, boots are not the best first item as it will be harder to start off with boots and win the first gank. Ninja tabi is also less useful if the other team has characters which don't depend much on their basic attacks. If you are against a team with a lot of crowd control abilities like cho'gath and cassiopia, it may be more beneficial to buy mercury treads.
All of cho'gath's skills scale on ability power and his e does quite a lot of damage if you play him as a dps, so, it is good to build cho'gath attack speed and ability power rather than attack damage. Since at the start, i have a lot of on-hit items, i prioritized the attack speed, rather than the ability power at the start. At late game, hextech gunblade is just so useful as it has spellvamp and high ability power.

Chogath's q skill is very important for the first battle. This is because if you can land a good q, you can immobilise the other team's characters for around a second and slow them for three more seconds. This is a lot of time as you can have a head start in the fight. I do not think getting e at the very start is the best idea as the q is much more valuable to be able to do. After that, you should get your e if you are going top as you will be having a lot of 1v1 and w if you are going bottom. After that, I prioritized r-->e-->q-->w, but the w is very useful if you are against skill based characters, so you should get w at level 2. If you want, you can level up r, the ultimate once, and leave it at rank one until level 17 if you only use that skill on minions, but I would not recommend it as cho'gath's feast can make you win a fight.

These are my preferred summoner spells, but depending on how you play and the opposition team, a lot of different summoner spells can work quite well. I use exhaust and flash. Because cho'gath is a slow character, he can have problems with running away. Flash is a good summoner's spell because of this. Especially if you do not want to lose your feast stacks. Losing your buffs and stacks can possibly result in your loss in certain situations as cho'gath highly depends on his stacks. Also, exhaust is just useful if you gank a lot or just when you are versing one other opposition character. Ghost can work instead of flash and ignite is a good general summoner spell.

Cho'gath is quite a good character that can be made quite uniquely. One thing is that this character should not be THE tank for the team and this is because even though he has feast stacks, he is very squishy for a tank. There should be another initiator.