I think you might need to soundproof the ceiling, not walls. If I am not mistaken the noise is coming from the 2nd floor through the ceiling.
I am doing something similar with my house, also in stages. One advise I picked up from here was to do renovations in small steps to maintain salability of the house in case of an emergency or need for cash for something else (end up in hospital, car breaks, etc). On TV shows they demolish everything 1st, than renovate, not good in real life.
I would start with the bedroom in the bottom left corner. This is minimal work - moving the door. Whoever is in there can sleep in the living for now. Move the door, soundproof, tidy up. Move back into the bedroom. Take a break.
Because you are removing the hall which has access to the bathroom, I would do the bathroom next. Add a new door 1st, add/remove walls, add soundproofing. Move appliances last. You want to have access to the toilet till very last moment :) . Take a break.
To expand the next bedroom once again add a new door following by walls and soundproofing.
Basically work bottom up from looking at the picture and add a door before walling yourself in. This way you will have clean area behind you at all times and messy working area in front, minimizing dust and mess transfer between areas.
P.S. use something like polythene film to hang around the working area so the dust doesn't go all over the house. I stapled it to the ceiling and taped edges to walls/carpet. No visible dust got out of working area.