For starters, don't jump and instantly say, "Newb, you can only get 6 items, not 7." The point of the guide is to go from jungle to an end match transition. By the time you're 16, given that you've followed the item build and skills, you'll be capable of going off and doing baron, solo. By the time you're ready to do that, you should have at least up to the rageblade; the bloodthirster if you've managed to gank a lot of kills during the round.
The reason I throw in the gunblade isn't just for the dual stat, it's the ranged slow and additional 400 damage that it can provide to this melee toon. However, the build itself can be modified with ease, yet I highly recommend, as Jax, keeping both the rageblade and the hextech due to their dual stat and giving Jax that extra edge to survive a 2v1 fight.
Whenever you're comfortable with being out and about, you can quickly replace the lantern with whatever else you may want to toss into it's place, in my case, I either throw in a Nashor's Tooth for the cooldown reduction, or the crystal scepter for the slow to all units. If you choose to be a tease, you could always replace it with a zhonya's and jump into a group of enemies when your team is nearby and use it's ability to force them to stop targeting you for a short while.
I know this isn't a great guide, but hell, it's been working for me and everytime I've jungled as Jax.
My jungle order usually goes:
Wolves (enemy territoy)
Banshee's (enemy territory)
Repeat above until acquiring a lantern
all other available jungle mobs, aiming to keep close to a lane with low HP enemy champs, ready to gank as needed.