A typical poured concrete assembly rates around STC 55. That is already good for most rooms; upgrades matter for theaters, studios and apartments.
Most effective upgrade
Build an independent stud wall in front with an air gap and insulation, finished with two layers of drywall.
Acoustic panels on the surface add only 1–3 STC points. They are for the sound inside the room. See STC vs NRC and flanking paths.