Before deciding, make a closing-week cash schedule rather than four broad pots. List the known payment dates for moving, insurance, service charges and the first mortgage payment. Then add only inspection work that cannot wait. Whatever remains becomes the emergency fund; furniture gets funded...
For someone still exploring, a “why rejected” column is surprisingly useful. Too far, uncertain costs, unsuitable layout, heavy work, poor comparison data—after a while it reveals your actual priorities better than a long wish list.