One of two routes for the Marks/Quints: I personally run AS/LS which is better late game but flat AD is also great for increased clear time in the jungle.
In most of the matches I am the exhaust carrier for my team and with Jax's Q being able to both get in or get out of situations I feel that I can sacrifice flash in most instances and get away with exhaust.
The mix of damage and tankiness makes jax a very strong threat in 3's and his tower taking ability is just unrivaled.
When jungling Jax I typically start dorans+boots and then wait for the pot in base. If the team is very heavy AD then I will substitute a cloth armor for the boots incase of a duel with their jungler or early fights.
After finishing the cutless you can either buy sheen or phage first out of the tri-force build. Both have their advantages and disadvantages and its more of a personal preference as to which you go first I feel.
Upon completing triforce and BOTRK assess the enemy team and see if you need more armor or MR for the teamfights and then build either Spirit Visage or Randuins accordingly. Most matches won't get past this many items as they are fairly higher cost, but if you get to a five item build and are thinking of what to build for sixth there are several options: Hextech gunblade offers so much more damage and sustain, if you went ninja tabi due to high AD and are having Tenacity issues you can always buy a moonflair spellblade which will increase your tankiness as well as give you that tenacity.