You might want to consider QuietRock for around the same cost. I'm skeptical whether it solves acoustic problems any better than carpeting and a suspension ceiling, but apparently it's price comparable and half the install time of double drywall. I think it's appropriate if you're trying to keep ambient outdoor noise out.
https://soundproofnation.com/quietrock-vs-double-drywall/If the basement is humid, I'd go for luxury vinyl plank over laminate, and don't skimp on the underlay. They're both photographic images of natural materials anyway. But a rug or carpet would be acoustical heaven.
