I like starting cloth, long sword and 3 pots. Boots really just aren't that essential early anymore, especially with how mobile Jax is with his Q. After that, my build goes as follows:
Grez's, Boots 1, Giant's Belt or Phage (depending on if him ahead or not), Ginsoo's, Boots 2, Frozen Mallet, and then my build is situation from that point on. Gunblade, Randuin's, Bloodmail, Maw, Lightbringer, King Blade, Bulwark, Sanguine, and Hydra are all good items on him.
21-9 or 9-21... both work.
Attack Speed Marks, AD Quints, Armor Seals, MR Glyphs
Skill order: E,Q,W,W,W,R,W,Q,W,Q,R,Q,Q,E,E,R,E,E
When laning, try to only trade when you have your E up. As a general rule, play passive until you hit 6. There are exceptions to this though, such as if you have a favorable match-up, or if they come to lane with little to no sustain. Once you hit 6, auto attack a creep 2 times, then QE auto the enemy champion for tons of free burst damage. You can do this over and over until you force them out of lane, or the opportunity comes to all in and kill them. With Jax, your focus should be on farming, not on trying to kill the enemy champion in lane. Although if your winning your lane hard and an opportunity arises to get a kill, by all means go for it.
Hope this helps!