I like the carpet also. I used regular carpet pad from Amazon underneath. I didn't fasten the pad at all. Just stapled the carpet over it. No homasote and no carpet ballast either. I'm sure that wouldn't hurt but it's already super quiet so not necessary IMHO. Here are some of my construction pics:
1x4 frame
1/2" plywood top
Carpet pad
Carpet
Today with sides and skirting (also from Amazon)
Good luck. Post some pics when you do it.