Hello
I'm building a shade only patio cover, it will attach to the house.
The size is: 12'x20' the 20'way is attached to, and across the house,
and the 12'is the distance out from the house.
The top cover consist of:
 1. approx.96-100 2"x2" spaced with 2" openings across the 20'way
 2. 13-2"x6" 14'long, (spaced approx. 21"1/2 appart) which sits on the
beam (12' out from the house) with  a 2' eve hang over.
 The beam will be 20' long with 2 post spaced under the beam at 16' apart.
 Question:
  What size beam/(not a lam beam) will I need to support this patios top weight.
  What size post will support this beam.
  I was told to use spruce whenever I can, your opinion. 
  Thank you

Your description sounds like the models on this site:
http://www.brinstallations.com/latticepatiocovers/latticemain.html

It appears that the dimensions for the pieces equivalent to your 2x6s
are larger.  This may not be necessary, but the visual impression may
be important:  it looks more substantial and permanent, the same for
using a beam with larger dimensions than may be necessary, ditto for
the posts.

Good luck