as mrbuffington said, builds and what you max are situational. don't get gunblade by the way, there are better items for jax.
if you notice other team as a lot of auto attacking champs, you can get tabi, and if other team has a lot off cc, get merks.
get triforce first in easy lane, blade of the ruined king in a lane you need the lifesteal and you can even start armor/mr if you really need it and get toher items later.
flask is often really good first since jax does use mana.
your late game build is going to look kind of like triforce, blade, boots, and then defence in most cases. again, you can start defence if you are having a lot of trouble in the start.
randuins and SV are good defensive items on jax. your last item is up to you. you can go even more damage if needed, or defence of your choice.
vs range, maxing Q is often good, maxing W if not range. what you start really depends on what you are fighting.