Gunblade and Sheen are my core.
I finish Gunblade before Sheen however. I like the extra damage on your W,R, and the spellvamp.
I love getting Triforce, but I don't get it every time, sometimes I build a lot of AP (Rylai's, Rageblade etc) and turn Sheen into Lich Bane.
A lot more expensive than the usual Triforce build, but you get hilarious burst on top of a big health pool.
Thing about Jax is, you can build absolutely anything on him. Triforce and Gunblade are most cost-efficient though.
Jax's damage output increases with AD, AP, AS, Crit and even CDR (less CD on W).