I have gone through many of champs so far, I find that Jax is my favorite, and usually when I play him I don't end up losing or going negative. If you have any concerns leave a comment for me and I'l get back to you.
If your going to down vote at least tell me why so i can improve on my build Because if you don't tell me your not helping the other poeple the would like to play Jax.

This rune page allows you to gain attack speed through your passive while still being able to take advantage of those hybrid marks and movement speed quint's.

These Masteries allow you at deal enough damage to creeps as well as those champs in lane, wile still having that defense and health regen for some added sustain.

This item purchase order is recommended if you are having a hard laneing phase and aren't doing so well I would suggest buying the phage first and then a sapphire crystal for added mana. If you're having a good laneing phase a good first item to build is the Guinsoo's Rageblade (get this in stead of buying a Hextech Gunblade) this allows you to be able to deal a significant amount of early game damage.

If you are doing Duo top or the jungler is going to go for an early gank go into Counter Strike "E" first because the stun will up your odds for an an early kill, If you clear enough creeps to level up go into Leap Strike "Q" second this will allow you to get even closer with your Counter Strike "E", and then proceed to max out Empower "W".

I recommend maxing out Empower "W" first this will allow you to deal a lot of damage early mid and late game. When using Empower "W" correctly weather on creeps of on champs a good Jax player will activate Empower "W" right after a basic attack allowing for an instant additional hit.

I recommend maxing out Leap Strike "Q" second mainly because no matter how many points you put into it you're still going to deal damage with its +60% of ability power.

I don't just recommend it I insist that you max out Counter Strike "E" last only because it is a one point wonder.

Flash is good because of the added escape beond the jump from Leap Strike "Q" and for chasing the enemy.

Exhaust is good to have especially for going into a battle solo up at top, for escape if you need to and flash is on cool down, and to set up a gank by your Jungler.

Ignite is good to pick if you aren't confident in your team's ability's I get this when doing solo queue. It is also good to use if you arnt confident in your own ability's in securing a kill. it can also be used for that added damage at the full build.

Ghost is a strong suit for Jax allowing him to be able so catch a running enemy after a team fight.

When farming and at least level 6 keep count of your hits becaus the passive in Jax's ultimate allows for high damage every third hit, with that being said after every 1st hit activate Empower "W" on a creep with high health maybe the siege minion this will allow you to instantly throw out another basic attack. When on your third basic attack go for another creep with high health.

The passive on Jax's ultimate allows for some high damage every third basic attack when timed well you can hit enemy champs for high damage