Certified PhD in architectural acoustics here, and I’ve been a mix engineer for half of my life.
I’m gonna echo everything Gutbucket says. You gotta seal up the space and add as much mass as you possibly can. Box-in-box construction is standard for many high end studios, and box-spring-box systems offer the best isolation IMO, though it’s obviously gratuitously expensive.
Owens Corning 703 is a standard. It ain’t cheap but it is effective when placed correctly. Personally since my grad school days I have taken medium to heavy weight blankets and cover them with boho shawls for building acoustical absorbers - much cheaper and aesthetically more in tune with my hippie sensibilities, and gets you most of the way there. Building the frame to be rigid and sturdy will be the biggest challenge. Air gaps can help, but only to an extent - they serve to “trap” waves with a 1/4 wavelength shorter than the distance between the wall and absorber, and keep in mind it’s still possible for sound to diffract around materials if you’re not careful in your construction.
My usual advice to people is, focus on making a good room better rather than trying to fix a bad room. The same philosophy carries over to mixing and mastering but that’s another conversation for another day. I get convenience is a thing, but trust me your basement will become a time, energy, and money pit if you try and wrangle it in to do what you want when that’s not what it wants to do. Reflections are not always the enemy, so don’t focus on making your room a sealed dead box if that’s not what it wants to do. Listen to the space telling you what it wants to do, and if it’s at a baseline “acceptable” sound then work to bring out the best in it; if it isn’t, I suggest you spend your efforts finding a good room to mix and master in.