Most of the popular Linux distros should work for gaming. I'd recommend Fedora or Ubuntu for being easy and tending to just work. I'd recommend against Arch because it's easier to break than most distros. KDE desktop environment can be configured to be lighter on system resources than gnome.
Really to know what you would like best and what works best with your hardware, you should make a USB with ventoy and add a bunch of different .iso files of different distros. Boot into the live environment and mess around, try your peripheral devices, etc. Be warned, live environments are significantly slower than a full install.
I would also recommend checking all of your games on protondb. If any don't work on Linux, you can dual boot.
$300-350 per month per person. This is about $100 more per person per month than we were paying during covid
$3/meal also costs more than what food assistance provides