Pros:

+Takes almost no dmg in the jungle thanks to Counter Strike
+Great gap-closer/escape mechanism through Leap Strike
+Low cooldowns late game
+Can be tanky with little armor/magic resist
+ Master-At-Arms is a large boost to your defenses
+Strong Duelist once you get ultimate
+Strong anti-carry

Cons:

-High Cooldowns early game
-Not very tanky without Master-At-Arms active
-No built in sustain

I choose to start with Counter Strike due to the huge dmg u can dodge with it.

Then i take Empower due to the dmg u get out of it. you will need it early when u go for the next buff.

And the Leap Strike is for ganks.

The rest is my personal preference.

You should always take Smite when you are jungling due to the chance of people stealing your buffs and the extra dmg early game.
You should only use smite when u know your Smite will kill the minion you are using it on.
You should also pick Summoner's Resolve when you are using Smite in the jungle due to the 10 extra gold u get each time you use smite.
You should also always try to secure the dragon and baron with Smite


I personally like to have Flash as an escape ability.
You can also use it if you are chasing someone, but only if you know you can secure the kill.
Since Jax dont have any escape ability i use the Wriggle's Lantern and Leap Strike to get out if Flash is on cooldown.


Ghost is also a good spell as it increases your movement speed for an entire 10 seconds, as well as avoid unit collision, allowing you chase after the enemy.
Ghost is also a nice escape ability.

CORE ITEMS

I personally like to start with Boots due to the extra movement speed you get and that will provide faster jungling for you. Later on you should upgrade them to Mercury's Treads or Ninja Tabi depends on what kind of team you are against. If they have a lot of cc you choose Mercury's Treads due to the tenacity. If they have weak cc you choose Ninja Tabi


Wriggle's Lantern is the most common jungler item and it is verry nice because of the free wards you get from it. Wriggle's Lantern is also a very good escape opportunity with Leap Strike


I choose to build a Phage because you get some exstra health and you get attack dmg.
And you get 25% chance to slow enemy's on hit.
Later on you should build it to a Trinity Force or a Frozen Mallet

MID-GAME ITEMS

I build a Sheen because it scales well with Jax 's Leap Strike and his Empower
And you will need it later if you are building a Trinity Force.


A Trinity Force is really nice for Jax due to the little ability power, slow , attack speed, attack dmg, sheen and healt he gets from it.


Hexdrinker is nice for the MR and the attack dmg you get from it.
If the enemy team deals alot of magic dmg you should buy this earlyer and consider a Maw of Malmortius

LATE GAME

Warmog's if just there to make u survive late game when the other team deals more dmg.


You build Maw of Malmortius late game just to get that extra attack dmg.


You build a Guardian Angel to get the extra MR and armour you need. +You get a extra life.