This is my Jax build that I have used for most of my matches recently. First of all the spells I chose can be switched out to your play style as I usually farm/gank in early game with lane partner such as heal which can be useful as he is squishy in beginning. On the skill sequence I really don't care for empower unless I get fed and can get my ability power up fast. Counter strike you need to get to level 5 ASAP since it gets your dodge up high with ninja tabi. My items are very interchangeable depending on the other teams combination of champions. If there is a lot of casters go for banshees veil instead of infinity edge or if you want your abilities to have a lot of damage I haved used zhonyas ring instead of infinity edge also. As most people say and should do is don't do exactly what I do, try my build out for maybe 1 game see how it works for you, maybe you need more attack speed change out an item or maybe you want more attack damage instead of ability power and take out rageblade for another blood thirster,ect.
Jax in the beginning is a great solo or partner in a lane. If you play it right like with a blitzcrank pull an enemy over and jump on him exaust and ignite and you can start out first blood in the beginning minute or so. Mid game run around and help gank and defend while farming due to most items costing a lot. Use your stun(counter strike) as much as possible when fighting and your ultimate will hurt them dearly when your Attack damage is high.
Good luck and if you have any questions/suggestions I am open to any ;)