Cho Gath needs 3 things to be good. Mana, Cdr, and health. Of course if you have mana lots of mana regen you don't need a lot of mana.

These builds focus on these points in one way or another.

I don't want to waste words describing cho cho. So here it is

This is sort of a niche build. I came up with it out of necessity. I noticed I would run out of mana in team fights. While out of team fights it wasn't a problem.

Pro's

Good early game. Not dependent on ganking.
Good transition to mid game.
Good support items.
cdr
High hp / mana regen. You won't need a second or possibly a third blue. A fact your mid will love.
5gp10

Cons

Not tanky early
Ganks may be a bit risky since you won't have much of a way to put out a damage or tank a lot of hits.
Wish it was a bit a more tanky.

This is what I build typically when I jungle cho.
Works well against Ad heavy teams. Which in is currently more likely.

Pros

Cdr
big mana pool
a bit more damage than the support jungler
Good against ad and ap

Cons

Low hp for a cho. But it does work well with your utl hp bonus
Low Damage. Only time you do damage in team fights is with your ult.

Very similar to Traditional but this works better against double ap or double ap + jungle
You need to choose what you want here.
Get movement boots if feel like you need to be in two spots at once.
If you get merc threads don't get Spirt of the Golem. You will get redundant tenacity and you would waste gold. I guess you could get ninja tabis if you want.

Aegis is always a good possibly but only if you have already have the cdr.

If you need armor go for Locket. Otherwise spirit visage for the cdr.

Pro's

BV makes you very tanky early
Lots of build options. Tankiest of the three builds

Cons

Can't tank turrets well early because of lack of armor.
Bad cdr early. If you do get cdr you have to sacrifice in terms of building a better item.
(spirit visage isn't great but it is cheap cdr)