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:
Masteries:
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.
4. Deathcap.
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.
2.AD build:
Masteries:
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.
Itemise:
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 
Later edit:
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