This is my favorite Jax guide. Regardless of which style I use, though, my first three skills are usually Leap Strike, Empower (for that cheap +75 damage to leap strike), then Counter Strike. Counter is too expensive to use early, and you're really not getting hit enough to sacrifice major harassing/kills early game. From then on just get it in the priority you prefer - I usually focus leap strike to reduce the cooldown and improve the damage. Second skill depends on enemies - empower if the enemy lacks in physical DPS (bad for you) or counter if they don't.
Also, regardless of style (or character for that matter) I almost always start with a philosopher's stone. It has good mana/hp regen and it pays for itself.