I took a look at your floor plan and found a number of similarities to my plans. I'm at the sound mitigation stage. I've completed framing and roughing in the plumbing and electrical. The exterior insulation is in place.
This A.M. I was working on the sound treatments.
First I'm putting up insulation in all ceilings and walls. Second I'm putting up the 1/2 inch Celotex soundstop board on all critical surfaces. For me that means the ceiling, soffits, walls adjoining other surfaces and the furnace room. It's cheap $6.37 a sheet at my HD. I plan on putting up 5/8 drywall on all these surfaces first then evaluating the sound control. If I'm happy that's it, if I'm not then I will add another layer of drywall perhaps mounted on resilient channel.
From my reading sound control is frequency dependent. Insulation and The soundstop work on the upper frequencies but for the bass it takes either extra mass (lead sheets or double drywall) or mechanical isolation (resilient channel or foam pads)
I think sound control planning is also related to lifestyle and plan use for the room. In my case it's just the wife and me. When we are watching a movie I'm not really concerned about what sound travels to the rest of the house.
However, I like to crank up the stereo and play along on my drums. My goal is to do this without having her complain.
Let's talk about stairs and something you haven't mentioned....the furnace room.
As for the stairs, looking at your floor plan I see that the sound source will have to make a 90 degree right turn and then go up the steps. Think of sound the same way you would think of a wave in pond. The way sound will get up the stairs is to bounce off the walls. So don't let it. Cover the walls and ceiling with sound absorbing material. Be sure the steps are carpeted and they use heavy pad. Try to insulate the stair walls to keep them from resonating. You may need to blow in insulation in the existing internal cavities. Put some sound treatment on the side of the door facing the basement.
The furnace. In my case I want a really quiet room to listen to music. Sit in your basement and listen to the furnace start up. In my case it's loud so I'm paying special attention to the furnace room walls and the ductwork. I ripped out all the metal round ducts and replaced with insulated. I'm gluing acoustical tiles to the exterior of the return vents, surrounding with a layer of insulation, using soundstop board and a double layer of drywall on the surrounding soffits. For the basement I built serpentine path return vents lined with egg-crate foam.