This is my first build so critisism would be nice. So first of all dont vote or comment until you have tried my build. This build is very amazing you can easily kill anyone.

Pros:
.Great 1v1
.Extremely high damage output
.Great in team fights
.Very tanky due to his passive and life steal
.Heavey carry
Cons:
.low range
.Squishy in early game
.hard to master

What you should have:
Ghost: great all around for escaping, catching fleeing champions, and for quick movement.
Exhaust: Good for early kills and escaping.
Ignite: Great damage usful for early kills.
Maybes:
Flash: good for that little extra range when attacking and great for escaping ganks though walls
Teleport: Good for ganking and for back dooring.
Cleanse: Good for escaping
Heal: Its an ok spell for turning the tide of a fight or saving a life or two but not critical
What not to get:
Revive: lol kinda obvious but this spell is just plain bad I think
Smite: you are not a jungler as jax
Clarity: Playing jax using this build I have never ran out of mana