Weather will be a crapshoot. Could be sunny, could be very cold and it will definitely rain.
I would say that it is not a really busy time of year, but the christmas market and the shoppers will be out in full force, so I avoid the Piazza Navona and via del Corso as much as possible.
We stay in an apartment, but there are lots of decent hotels near the centro storico, I haven't stayed near the vatican, so I can't comment.
If you have never been to Rome, I suggest taking a walking tour to get yourself oriented.
bon viaggio