I can't tell whether the dress is burgundy or plum velvet. I am guessing it is burgundy velvet?
However, yes - That is nice for NYE. The cut of the gown is classic & simple, so you can vamp up the makeup, accessories a bit. Out of the options you gave us, I would pair the dress up with the black strappy heels on the far right & the simple rectangle evening bag on the far right.
For makeup & nails: I usually like a French manicure each day but, a deep wine/ merlot would be nice for NYE on the nails. I would also do some sort of berry/ burgundy on the lips with big diamond studs, tennis bracelet & pull my hair back to accentuate the shoulders.