You need to be a bit careful in selecting sound dampening materials and techniques. The ability of pretty much all of the techniques/materials is quit frequency sensitive. It is unlikely that a single fix will deal with the sound levels you are generating.
The high frequency components of a gun shot are relatively easy to reduce (not easy). I believe there is a large component of very low frequencies involved in a gunshot (someone chime in if this is not true). Those are hard to reduce and could be some of the more annoying parts of the sound. In home theaters, the challenge of sound isolation is what the woofer/sub-woofer produces. Stand outside of the house of someone who has a sound insulated theater adn note what you hear. Be sure to look at the frequency curves for any selected method. This does indeed head a bit toward rocket science if you actually try to figure it out yourself.
Wall stuffing tends to deal with high frequencies. Isolated walls (if properly done, with stuffed walls) help more in the LF sound. The material I mentioned for between 2 sheets of drywall (sorta green and comes in caulking tubes I think), and expensive, I think do reasonable well at LF (it has been many years since I looked at this stuff). Depending on what is in the ceiling, getting wall isolation could be a real pain (and you still stuff the inside). The goo between panels is relatively easy to apply. I have this dim recollection it is called green goo; but I really am not sure. If you are interested, I might have a left over tube stashed somewhere and I would try to find it).
You need to remediate anything that penetrates the sound confinement area. Doors should be exterior construction. Airtight. I used fiberglass cores. I am not sure if that is the best approach. There are probably doors made specifically for this; but probably very expensive. Any conduits or HVAC entering the controlled area need to be dealt with. An airlock set of doors could help. That is what I did. The isolated walls are so-so. The rocket scientists I had for builders, aside from having to constantly explain water flows downhill, did not follow instructions since granddad did not do it this way. You really have t be on top of things. They will have no idea what is important. Everything that penetrates the sound barrier needs to be fully caulked with special sound barrier caulk. That mans you caulk multiple times in the same place depending on your structure. You caulk each layer; not just the last one. This is not simple or necessarily easy to be done right. And you do not generally have an effective second chance.
