Regarding black ceilings -- when I built my first theater, my wife and I were debating whether to paint the ceiling black or not. The concern was that it would feel too closed in, gloomy, etc as has been noted in this thread. We went to visit someone else's place that had black ceilings and loved it - the ceiling just "disappears" and you don't even notice it's there.

Since you're concerned with sound, I'll put my vote for "remove drop ceiling, put regular insulation in the joists, and put up some drywall. If you want to get crazier (like I did), you can -- I built backer boxes around my lights, decoupled the drywall from the joists, used two layers of fire-rated drywall, and used green glue between the two sheets), but for a simple game room, that's probably not necessary.

I did the walls as well as the ceiling. I also did stuff like putty pads on all of the electrical/low voltage boxes, extra weight put on the ducts in the ceiling to stop them from vibrating, etc. And you're right, it was way more expensive than I was thinking - but ultimately it was worth it because I can watch a movie (or play pins) in the basement and my wife can't hear anything in the room right above unless the subwoofer is really rocking - then she says that it sounds like "thunder off in the distance." Win!

I also didn't connect the room to the house's HVAC system, instead putting in a dedicated minisplit for heating/cooling, and a dedicated air exchanger to get fresh air in the room. Ultimately, the air exchanger is probably the weak point in the room for sound escaping. Most people think I'm a little crazy for going to this extreme, but hey, I'm happy with it and it works well!