That valve uses Arch is irrelevant in all honesty. Proton is not a Valve product, Valve is merely one of its users and contributors, and it is not wedded to one distro…Similarly Valves own Steam packages are not distro specifi, and there are other gaming platforms to consider which also benefit from Proton (for example you can get Gog windows games working in Linux too quite easily), as well as all the Retro gaming options.
Pick a distro you personally like. I use Mint as I like the cinnamon desktop interface and the distro is pretty much good to go from fresh install. I use Mint both as a dual install with Windows on my PC and also within VMs in Windows. I still spend a lot of time using Windows because of specific games compatibility and work related apps.
EndeavourOS seems a good choice if you do want to go the Arch route but it’s only something I’ve played with in a VM.
If you want something gaming specific then Draugar seems like a good choice - it apparently uses Ubuntu LTS but with the mainline Kernel updates optimised for gaming. But I have no personal experience with the distro.
I also see a lot of people seem to like Pop!_OS, but again no personal experience.
I’ve had no issues with Mint on my setup.
You may have the GPU drivers installed but are they active? Look in “Software & Updates” on the Additional Drivers tab and see which drivers are active.
Installing the drivers is not enough, you have to select them to use them too.
If the latest drivers are active then you may need to think about switching to a legacy version (you have a pretty old CPU and GPU by current standards; newest drivers are not always best). You may also want to look at using older versions of Proton than the latest for similar reasons - there may be features and changes in newer versions that are just not going to work with your set up or your set up just isn’t tested to work with.