What type of lattice should I use for a privacy screen?
I would recommend you build it yourself.  None of the building supply versions that I've seen can stand up too much more than 3 years of weathering.  They use cheap fasteners that rust and stain the second year.

Self construction will allow custom size openings.  Weaving is another possibility.

Teak, ipe, redwood and cedar, in that order, would be my top choices for natural or stained.

Stainless fasteners are a must.

Lattice construction atricle  

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