If you are Hybrid jax here is the standard buy order along with swap outs.
Jungle ludens - Boots - Hextech gunblade - Lichbane - Guardian Angel - Guisnoo's rageblade
Need MR? Spirit visage over Maw of Mor & Mercurial Scimitar unless you want more damage or keep getting stunned.
Need armor? Randiun's omen, Sunfire cape, or Dead man's plate.
Need to be just more hp because your ult gives you enough mr and armor? Sterak's gage+Frozen mallet are my favorite two items together for jax.
Because jax's ult passive gives mr and armor but not health, health is the most important tank attribute, it also blocks physical and magic damage the same. If you ever need to buy any mr or armor item make sure it either has ad and kick *** bonus effect, or health.


Ap Jax jungle Build order
Ludens jungle item - Boots - Hextech gunblade/Nashor's tooth - Lich bane - Rabadon/Nashor's tooth - Void staff. If you want to go full ap just cause or because your team needs it here is what I recommend. because Hextech only gives 80 AP and we need magic pen, I usually sell for void staff or don't buy. If you do not buy hextech gunblade you have two options as a second item that will allow you to Gank, be relevant, and clear your jungle. You can build Nashor's tooth or Lich bane second. Nashor's is safest route, cd, as and on hit for jungle. If you plan on ganking a lot, like me, get Lich bane. That way kill solo camps Red/Blue/Gromp/Scuttle/sometimes wolves and gank, instead of waste time trying to kill all the little krumps and wraiths.
Ap jax has much less build room since he needs so many core items. Other ap items to build are hourglass, abyssal scepter, and hextech gunblade. That is pretty much it.

Ad jax build order
Jungle ad item - Boots - Triforce - BoRk - Frozen Mallet - Sterak's Gage.