So when I started thinking of Jax's Passive Turning a Percentage of his AD and AP into health I started to create the ultimate guide. Let me explain.
At the beginning of the game, get "Doran's Blade" Try to pickup a few kills and at least get 20 minion kills before you recall. When you have enough money buy "Ninja Tabi," it's good for dodging minion attacks so you don't lose as much health laning also, buy"Health Potion x3". Try to pickup as many minion kills as possible before recalling.
You should be around level 6 so, now you work harder on your build. If you have lots of money saved, build either a "Phantom Dancers" or a "Guinsoo's Rageblade" for some good AS. Next you start building you AD, I highly recommend stacking "Hextechs Gunblade x3" (for passive purposes) then sell your "Doran's Blade" and build an "Infinity Edge." (This is why I recommend "Phantom Dancer's.")
My Masteries I use "25/3/2," because my runes, help with Defense (Dodging, Health, Armor, etc.)
The spells I use are "Ghost" and "Exhaust" they can be very useful for picking up runners and getting out of sticky situations in beginning-game.
By the time you finish this build, you should receive over 600 Health with his passive, because of the "Hextech Gunblade x3."
If you have any suggestions please don't hesitate to post, I would appreciate anything I have missed regarding the build itself, but this was designed to fit my personality of using Jax so, anyways thank you for viewing my guide I hope it helps, somewhat.
Regards, -Raptures End