Advice on Ceiling Sound Reduction for Basement Reno

We're doing a Basement Reno. The space will have a Bedroom, bathroom, laundry room and the rec room area will be around 20' x 20'. It will primarily be used as a home theatre, but not exclusively. It's also the main space that everything is connected to, so will have the stairs up, doors to laundry and bathroom, as well as the entrance to a crawl space and door to a cold room.

I'm not concerned with the walls as I don't need to worry about disturbing anyone else in the basement, I'm most concerned about the noise escaping from the basement upstairs to the rest of the house. I'm looking for the most bang for the buck.

There is a post and beam in the rec room, so I'm concerned this will be hard to properly decouple. I'm also looking to mount a projector & screen on the ceiling, 2 in-ceiling speakers, and perhaps 2 rear surround speakers may need to be mounted on the ceiling as well. There will also be many potlights. I'm also using a contractor who doesn't specialize with soundproofing rooms. For these reasons I think I'm not going the sound clip route (although I could be convinced if someone can make the case it would be worth the additional expense).

Right now my contractor is recommending hat channel (he calls it U channel) with 5/8" Quietrock and Safe n Sound for the ceiling. I've read many suggest I could save with pink insulation. We'll also add a solid core door to the basement entrance. Would this be a decent solution?

any thoughts would be much appreciated.