Cho'Gath is a very fun champion to play that is very versatile in his roles. He can play an AP champion that can act as a nuke, a full tank that is nearly impossible to take down, a jungler, or my favorite, an offtank. This build will highlight Cho'Gath as an offtank because I believe it is the best type of build for the champion.

Pros:

A lot of CC
Good base health with

Feast
Nuke with Feast
Extremely Big with all of his feasts. which makes it hard to target smaller allies
Vorpal Spikes help with small AOE damage
Good regen with Carnivore


Cons:

Mana problems, especially early game
Two main abilities are skill shots

Offtank Cho'Gath is best fit for top lane. He can duel it out with the other top lane and can push when needed. He will be very tanky at the start and cannot get harassed that much. This will also enable Cho'Gath to get a nice farm. Cho'Gath is pretty dependent on items and the quicker he can get them the better.

Bot lane is an alright option but you will be facing a ranged ad carry and a support. During the laning phase, Cho'Gath's worst nightmare is a ranger ad carry. He can be harassed multiple times while his spells are on cd. Also the ad carry that you are laning with should get all of the farm. This means that you will get items later than practically everyone else and not be bulky or powerful.

Cho'Gath should never go mid because he will usually go against ap carries that will just outrange him. His skills can be easily dodged from far away and Cho'Gath can be kited pretty easily.

My choices:

Flash
Flash is a great spell because it could get Cho'Gath out of a lot of bad situations. If you overextend, need to escape, or need to chase after a teamfight, this spell accomplishes it for you.

Teleport
Teleport is another useful spell, especially since Cho'Gath will go to top lane. If Cho gets harassed and needs to go back, he will teleport back in seconds without losing any farm, experience, or the tower. It can also help if he Cho'Gath is low on mana. Lastly, teleport can help in pushing/defending turrets. Late game Cho'gath can take out almost the full minion wave with Rupture and [feral scream]].

Other options:

Clarity
This can help if you find yourself having mana problems because you are new to Cho'Gath. It is helpful early game but useless late game because items take care of your mana problems.

Ghost
Another good escape/chase tool that also has utility of getting around the map quicker. I find flash a little more useful though.

Marks:

Greater Mark of Magic Penetration
All of Cho'Gath's abilities are magic damage. These magic penetration marks will tear through some base mr of champions and will help you do more damage.

Greater Seal of Armor
In order to succeed at top lane, Cho'Gath needs to be able to take a little bit of harass. With these flat armor runes, it solves the problem of laning against bulky ad melee champs.

Greater Glyph of Magic Resist
These glyphs have the same purpose as the seals except these flat glyphs helps you if you are laning against an ap solo top. You will be protected from a gragas or fizz who has 50 ap at level one and not be torn to pieces.

NOTE: These runes are just the optimal ones for Cho'Gath in my opinion. Since runes are expensive, if you have a similar tanky rune page, that will work well.

Cho'Gath is mainly a tank so I go 0-9-21 in masteries. In defense, it is helpful to take flat armor, flat magic resist and health early on. Later in the tree, it is helpful to get movement speed to intitiate/chase and cooldown reduction. The final mastery in the tree gives a big health boost to Cho'Gath, and gives him free tenacity. Utiltiy improves Cho'Gath's two summoner spells and helps with mana problems. Also gives a slight movement speeed boost and longer buff duration.
I feel that offense does not really help Cho'Gath too much so I suggest you stay away from it.

Passive: Carnivore
This passive is extremely useful in the laning phase. It basically gives you an added benefit to farm. Not only will you get gold from killing a minion, but some health and mana to help your sustain. A pretty good passive for champion that goes top lane.

Q: Rupture
This is a very disrupting spell for Cho'Gath as it launches enemies in the air and slows them. It is arguably his best cc except the only problem is rupture is hard to land. When cast, the spikes show on the ground first and then pop up after a delay. This gives enemies a good amount of time to dodge the spell. This spell is great for initiating a team fight as it slows the enemy team and renders them helpless for a couple of seconds.

W: Feral Scream
I love this spell with a burning passion. It his a pretty high damaging AOE silence that silences champions for 3 seconds at level 5! It is pretty easy to land and has a pretty good range. In teamfights this can sometimes be used to just decapitate the entire team, especially the mages. Use this spell after you get a hit with rupture.

E: Vorpal Spikes
This spell is a free toggle, which is always good. When Cho'Gath auto-attacks, spikes shoot out of his mouth damaging nearby enemies. They do a small amount of damage but work really well with Rylai's Crystal Scepter.
Quick note: When auto-attacking a tower that is being defended by an enemy champion. Make sure to turn vorpal spikes off. They will hit the enemy and you will take aggro from the turret. Just remember to put the spike back on!

R: Feast
One of my favorite ultimates in the game is feast. It does a high damaging nuke that does TRUE DAMAGE! That means it can't get negated by any armor, or magic resist. Another amazing part of the ultimate is that if the feast kills the target, Cho'Gath gains a stack of maximum health that stack six times. It also makes Cho'Gath bigger with each feast. An important note is that this spell should first be used on minions just to get the stacks up. When you have six, you can use it freely to deal massive damage to a carry and so on. The other great aspect of this ultimate is that it acts as a super smite. It does 1000 damage to a minion so it is great at stealing/securing dragon/baron or blue/red buffs. The one drawback is that you lose half of the stack upon death, so be careful!

I max Feral Scream first before rupture because even though rupture is more disruptive, it is harder to land. Feral scream is easy cc that can do a good amount of damage and silence opponents.

I max Rupture second because it still gives a lot of damage and slows enemies a lot. It is the most damaging spell you have other than your ultimate, but its unreliability hurts it.

I max Vorpal Spikes last because it does not do a lot of damage. I do get one level of it early at level two though because it helps in poking at the opponent in lane and helps hit minions too.

I max Feast whenever possible because of the aforementioned benefits it gives to Cho'Gath

Starting Out:
Ruby Crystal
This gives Cho'Gath a nice boost of health at the beginning and lets him stay in lane for a good amount of time before going back.

First time back:
Catalyst the protector Boots
Try to save up 1200 gold to get a catalyst and boots. The catalyst gives you a little bit more health, mana to help mana issues and a nice passive. The passive lets you get 250 health and 200 mana over 8 seconds which helps your laning phase monumentally. Also, basic boots help movement speed to dodge skill shots and to chase and escape.

Finish Early game and Core Build:
Mercury's Treads Rod of Ages
This is the beginning of your core build. The merc treads give nice mr and tenacity, which decreases disables on your champion. Rod of ages is an important item for offtank Cho'Gath because after its stacks, it gives 80 AP, 630 health, and 750 Mana. I get it as my first non boots item because it is important on finishing the stacks early since they are time based.

Mid Game:
Rylai's Crystal Scepter Randuin's Omen
Another health item here that gives 80 AP and 500 health. What is great about this item is its passive. Upon attacking enemies with spells, it slows them by a certain amount. This works with vorpal spikes too so Cho'Gath's basic attacks slow too. Randuin's Omen is your first armor item that also gives cooldown reduction, health regen, and small health. It also gives a nice active that slows movement and attack speeds of enemies around you and a passive that accomplishes the same feat if people attack you.

Late Game:
Force of Nature Zhonya's Hourglass

Force of nature is your main magic resistance item as it gives you 76 magic resistance. It also gives you a great passive too. You regen .35% of your maximum health per second. It may not seem like much but when you almost have 5k health, it is a lot. This item is a must on Cho'Gath. Zhonya's Hourglass gives you a whopping 100 ability power and 50 armor. What makes this item very good is it puts you in a stasis for two seconds. If you start getting targeted so much that you run low on health, activate it and you'll be fine. You can regen health in the stasis and end up surviving the teamfight if you teammates can do damage.

Other options:
Abyssal Mask
This gives you some more magic resistance if the team is ap heavy. Along with giving you some ability power it also lowers the magic resistance of nearby champions to help your damage output even more.

Ninja Tabi
If the other team is very ad heavy, switch these boots. Only do it if they have more than two ad carries because the tenacity mercury's treads is so helpful.

Frozen Heart
Only use this if you are having mana problems. Replace Zhonya's hourglass only if you constantly find yourself running out of mana. It gives nice cdr and a cool (no pun intended) aura too.

In lane, focus on your farm as much as you can. Do not worry so much about getting harassed a little bit because getting minions kills gives you regen for both health and mana. This gives you gold, added sustain in lane, and more mana to harass!
If a rupture hits an enemy and you initiate the team fight, do not use feral scream right away. Wait until the rest of the team engages and then silence most or all of the team. If this hits the ap carry and the tank especially, the team is pretty much shutdown for three whole seconds.
When feast is at six stacks, do not use it only for last hitting champions. Try to use it quickly on the carry so that they can die extremely quickly.
Lastly, don't forget to buy wards! As a tank you need to give your team vision. Make sure you ward your jungle, the enemy's jungle, and pink ward baron and dragon whenever possible. You may need items but the carries need them even more!

This concludes my build to Offtank Cho'Gath! If you read through all of this, wow thanks!
If you scrolled through that is ok too!
Before rating I would appreciate if you try the build out first and see if it works for you. I put in a good amount of time into the build so I hope you can give my build a couple of tries before rating!