I think for ganking potential you should get Bilgewater Cutlass before Phage for the active slow, and the life steal will keep you more sustained then the 200 hp from Phage.

I have considered and tested out building Spirit of the Ancient Golem instead of the Spirit of the Elder Lizard but the problem is, it doesn't give you the snowball potential that you need to carry as Jax, and the DoT is too handy to give up. I have had countless kills where the enemy flashes last second and dies to its DoT. It synergizes extremely well with Jax. As for the Trinity Force and Blade of the Ruined King, they are very important on Jax, Trinity Force provides multiple stats such as AP, crit chance and the MS boost to help you stick to your targets. Blade of the Ruined King's passive is very handy when it comes to late game because you can take down tanks, it helps you stick to their carries and the attack speed it provides is very powerful for taking down objectives, split pushing and dueling.

TL:DR I find my core to be too important on Jax, to give up one item for a little bit more survivability.

I will add more defensive, situational items, but they would just replace Randuin's Omen and Spirit Visage. That's part of the "Under Construction" part of my guide.

As a jungler, you should always know that you need flat MR runes unless the enemy has very little AP or no AP at all because although you don't face any AP in the jungle, when you gank mid you run the risk of getting instantly bursted or their mid roaming with their jungler into your jungle.

For the "First Back 800/1200 Gold", I will change that ASAP.

As for the masteries concerning the Warlord , the bonus damage is not that much and I find it more effective getting some AP, specially considering Devastating Strikes . Jax greatly benefits from both AD AND AP.

When it comes to percentages, you need to understand that they are only effective when the numbers being effected are high.

Bear in mind this mastery only effects bonus attack damage. On my guide you build Spirit of the Elder Lizard, Blade of the Ruined King and the Trinity Force. That's 85 AD, with the masteries and runes, is 108.8, or ~109 AD. ~109 AD plus the 5% is 114.24, or ~114 AD. You'd be getting a bonus of about 6 AD.

If you were to grab Mental Force and Arcane Mastery you will get 22 AP by late game. Early game you would have about 6~9. Trinity Force gives you 30 AP, so you'd have ~109 AD and 52 AP. Have you ever ganked a lane and the enemy escapes with barely any health? That small AP boost is going to give you that humph that you need to finish the job. Late game it makes a huge difference because it makes it even harder to itemize against you. Flat amounts of stats is better than percentages.

So, do you want to have 6 more AD, or 22 more AP?

Don't get me wrong, Warlord is a very good mastery, but on champions that build a ton of AD, like Riven, Yasuo or an ADC.

By the way, the guide is still under work. The core is down.

"Guide still under construction

I will add more in-depth information as soon as possible."

(Looking at cheatsheet only cuz i gots no time >< sry)
I think you could add a few scaling MR glyphs since you won't be facing ap damage in the jungle
doran's blade is 440gold so I think the variation of first back gold is 800 to 1240 :P but actualy the first back is 910 gold (yes i deducted the price of machete) and 2nd is 1350 :)
-> Priority item notes... what do you mean by "by now"?
The AP mastery don't make much sense to me, I think you should get Warlord instead for the bigass ad boost.
The guide looks very short and doesn't seem to contain a lot of information

I like your starting even though I think you should probably build just two offensive items as core followed by defensive items. You might wanna add situationals like Guardian Angel, Banshee's Veil or Maw of Malmortius (I'm not so sure about these).
Not to mention that you should take a look at this guide for coding and stuff the Rune Planner and Mastery Calculator to make your guide more appealing and so readable.