Feel free to experiment with the build, masteries, ides and most other things.
But what goes in this section is the essentials-must-haves-no-questions-asked section.

-Ninja Tabi.
-Flash
- Remember to FARM!

Pros:

- Jax is OP
-2nd best farmer(Cho is number1 XD)
-Fun to play
-AD or Hybrid
-Simple to play, and simple (with practice) to master.
-Great Carry

Cons:

-Not many escape tools. (But that's why you have flash)
-Cant think of much else...

Dorans.
It gives 3% life steal you start with 56 Attack, So 7 health a hit help in-lane and added attack damage.

Recurve bow. This is mostly just so you can build it into the Sword Of Divine. But it does add 60% attack speed witch is AWESOME early game.

Sword Of The Divine. Jax is an early game assassin and late game penta-killing-baron-soloing-turret-tanking machine of doom. For the early game with this item your attack speed is boosted incredibly. This item has an effect giving every fourth attack 100 magic damage.

Ninja Tabi. This item is just a MUST. The situation does not matter, no other champion in the game relies on there shoes as much as jax. The reason behind this is the 12% Dodge.

Guinsoo's Rageblade. This is one of my favorite items and jax equipped with this can out-farm any champion in the game. (Actually cho' gath but oh well)

Hex-tech gun blade. Due to the recent debuff this item got pretty much not viable on any other character. Except Jax. Jax even though i am still raged it got debuffed so bad STILL needs this item.

Atma's. You will have 2,500 health by now and this item will boost your AD very well.
(By almost 100)

Rylai's Crystal Scepter. For a last item you can get a rabadons, infinity's edge, blood thirster, black clever or maybe even a trinity's force. But this item is probably the most intelligent. (But the others i listed are situational and could be better. Up to you and your judgment)

Jax is an INSANELY AWESOME FARMER. When in-lane remember, jax is meant to be farmed. I don't have much on farming, but the items in the build (Guinsoo, Sword of divine, Rylai)will help you become a GREAT jax. Because a farmed jax,(In most cases)is an Auto-Win jax

I play jax quite a bit but he is not a good ranked. Jax is mostly good against, well, noobs.
The ONLY reason you should play ranked is if you think your real good. Because they with have played against many jaxes and understand how the stun works. Only play ranked if you are confident in your skill.

Thanks to Senraise for helping and the Sword of the divine idea, and the runes.
Inspiring me to play JAX