A typical double-layer drywall assembly rates around STC 45. That is already good for most rooms; upgrades matter for theaters, studios and apartments.
Most effective upgrade
Decouple one side with resilient channel or sound clips, or add damping compound between layers.
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.