This isn't a guide, just something i think may help. To install Steam on an Arch-based distro in most of the cases a simple sudo pacman -S steam will do just fine.
The installation will ask you to select a valid vulkan package from a list. And in most of the cases that's just fine... most of them.
Then you have your very "picky" old nvidia GPU which works only with a specific old nvidia driver and if you try to install anything else, there will be a conflict. Now you can try to remove the old (working) drivers and try your luck. But looking online i find a simple way to skip this passage and install Steam.
sudo pacman -S steam --assume-installed lib32-vulkan-driver
Nvidia supports 13 year old hardware and newest kernels with 580. At some point when running your 14 year old GPU one might consider just running the open source nouveau after all I assume that if you are running a 14 year old GPU you probably don't need the utmost possible performance or you might consider getting a 4 year old AMD for $100 to replace your 14 year old nvidia.
Whilst it would be ideal for you not to have to look up anything ever nvidia will tell you which driver to use with your hardware
https://www.nvidia.com/en-us/geforce/drivers/
If you are feeling frisky you could synthesize the already available data into a script that tells you the same thing. Linux Mint has a GUI for this which tells you which version is recommended for your hardware and your total commitment is clicking install and rebooting.