What is the best glue to attach raw linen to basswood? Also let me
know what other choice I have.

Maybe this is supposed to be for a secret Christmas present, but if
you could explain a bit more, it would be helpful.
Is the linen just covering the wood (such as the surface of a box, etc.)?
Or is it something like the canvas for a painting, a frame with the
linen under tension?  (This is usually fastened with a power stapler.)
Must the glue not be visible when dry?

Can you clarify for us?
regards, Myoarin