I would add, if you stain before installing, you need to apply atleast 1 seal coat also - this will prevet the stain from getting messed up during handling. My normal SOP on stained homes is to stain, spray sanding sealer, let the carpenter install, touch up stain as needed, putty, sand,dust, apply varnish,sand and recoat as needed.
As a diy project, I believe you would benifit from sanding and apply the 2nd coat of poly before installation. I agree with XSleeper that it makes mnore sense [quicker/easier] to stain and finish before cutting. Unless you sand any exposed cuts they will stain darker, I often cheat by thinning the stain some for those areas
