There's something on lds.org in the Serving in the Church area that tells you what the new meetinghouse library gets for a startup kit. You may want to coordinate with those in the old building for certain things such as any music your ward bought that was in that library, etc., to see what you want to leave and coordinate on what you might want to take. Consult that list for the things that should stay due to the materials that will be provided for a startup of the new building.
As to the move, ten years ago we moved into a new stake center, I think we took the computer (MIS), but left some furniture including a large desk used for the bishops office, as the building had the more commonly used table desks you have seen the last few years.
We used a ward welfare council meeting to go over what the new building had and didn't have, went over where things would go, and even how much space was available in the closets. It was a bit less than what we had in the old building, which was a newer one that replaced a legendary structure in Provo some years earlier although it still stands it is no longer owned by the Church.
In the end, we had it all set to go and moved it in one evening.
Even then, everything that others have described about the readiness for use of a new building, including equipment, the meetinghouse library, etc., was essentially the same.