I played Jax alot, even though I don't currently own him (I intend to buy him in a few minutes or so :P ) and these are two builds and masteries I like to use:
1. AP build:
9/11/10 with 15% magic pen in offense, nimbleness and full armour and magic resist bonuses in defense and time spent dead, bonus exp, greed and a bit of mana regen in utility.
As summoners spells, I would use cleanse and exhaust, but it is not a textbook to follow.
As items :
1. Cloth armour +2 h pot + 2 mana pot.>>>Ninja tabi's.
2. Hextech revolver>>> Hextech Gunblade.
3. Sheen>>> Lich Bane.
5. Rylai if you need an extra CC, Void staff if they start to stack magic resist, especially effective versus tank teams.
6. Deathfire Grasp if they have a very unkillable Cho Gath or another tank alike.
9/21/0 with 15% magic pen in offense and nimbleness, full armour, magic resist bonuses, veteran scars, damage reduction bonuses vs monsters all the way down to AS and AP bonuses, 4% damage reduction.
1. Cloth armour+2 h pot+2 mana pot>>> Ninja tabi's.
2. Vampiric scepter>>> Last item morph into Bloodthirster.
3. Sword of the Divine asap.
4. Madred Bloodrazor.
5. Wit's End, if at least 3 mana champs in enemy team, or Guinsoo Rageblade.
6. Infinity Edge, before Bloodthirster upgrade.
As summoner spells, I would choose either the previous Cleanse+Exhaust, either Ignite+Exhaust, with improved Exhaust in each case.
Hope you have fun trying those. Just my point of view.
Have a nice day all
Runepage is the same for both builds :
Dodge seals and quints and full attackspeed Marks and Glyphs
Someone can't take another opinion but his/ her own : ))
It's good to know we will never save this damned planet :P