No worries! We all have a story that gets us here and I am glad your wife agrees with the VC choice! The dualtime should work perfectly with the VA Beach and Beijing back and forth especially since both are on hour increments (remember you can't do half and quarter timezones with this one). In terms of your questions, here you go:
Since its a recent watch you should get a passport-sized booklet (black with Vacheron Constantin Geneve in gold lettering). When you first open it there is a guarantee certificate in a transparency containing the passport number and stamped with a date; your guarantee runs two years from that date. The Passport will have multiple pages. Of interest is Page 3, which contains a picture of the watch, the name of the collection and the watch's name (so here Product Family would be Malte and Watch Name would be something like Dual Time). On Page 5 you will have the full reference number (per your info, it would be 47400/000G-9100 in this case). You will also see two distinct serial numbers (in the 6-7 digits) one is the case number and the other is the movement number. The page should also contain other information such as material (here 18k white gold), dial type, and strap type (here Black Missisisippiensis alligator).
Note that the numbers on the caseback itself will be the reference number (47400) and the case number. The movement number will, if I am not mistaken, be on the inside -these should match the info in the paperwork. Also note that the watch should come with a folding clasp and not a tang buckle as well as a corrector pen.
As for the movement cal., it won't be on the case or any of the paperwork. If you pop the watch open, it should say "1222" on the movement itself.
With regards to the plastic bag, usually new watches are factory sealed, so they would come in an elongated transparent plastic bag that is about the same width as the watch (I would not have it any other way!).
Happy shopping and looking forward to your picutres!