I found Skype to be the easiest to use with these requirements. I hosted a Jackbox game and was able to share my screen (and game audio), my webcam (albeit in a smaller view than normal), and could see everyone in a gallery view.
I tried Skype and it fell short as well. While sharing my screen I can only see a small floating window that shows 1 participant at a time. I can't see everyone while sharing the game. It was very easy to share my desktop audio while sharing the screen though.