Had a look at the pattern envelope online to see if your fabric was on the recommended list for the stye.
For the proposed lining, sew the lining pieces for the bodice and skirt together, then try staystitching (sewing at 4/8" line) the lining (so right side faces the inside area where your body will be), wrong side facing wrong side of the satin, to the armholes and neck area BEFORE sewing on the neckband.
Your strategy seems sound. I don't know how one lining (if it is synthetic, to a synthetic fashion fabric) can reduce the static electricity or cling of the fabric (try ensuring you apply moisturizer a good 30min on yourself before handling your dress to wear it, or rinse your dress in a final water with some fabric softener in it).
