I'm going to just stick with my theory that the giant chains were part of the original plan (scale the walls by having the giants thrown the chains up top, or use them to pull the doors down or even chunks of the wall itself) and the Night's King just capitalized on an opportunity. Whether or not he had any idea there'd be Dragons coming when he surrounded Jon an Co was a bit irrelevant - the WW don't age or need food, so watching Jon Co die of exposure was perfectly fine by him. They're on horseback, so having the lances makes sense.
That does leave open the question of what they were going to do about the wards on the wall, but that could explain why NK waited until this point to move on the wall in the first place- the wards were broken, be it by age or by him marking Bran and then Bran going through the wall again. The old Three Eyed Raven was too cautious to break the magic in that way, and Bran is too inexperienced to have known. He had been building an army to invade for years, but needed that last piece to fall into place. Since he clearly has some green-seer powers of his own (since he can knock Bran out of his green sight), this might have been a very long struggle against the old Three Eyed Raven's powers that the NK finally got the upper hand on.