For games it probably doesn't matter, though with parity you will get a clear massage that something is wrong with your hardware ("parity error"). Most 30-pin simms have parity (and for very old PCs DIPs were always configured to provide parity - or at least i've never seen one without), 72-pin simms with parity are more rare. Also some PCs require to use parity or ECC ram (IBM PS/2 series).

It looks like I'll be going with non-parity. The cheapest parity memory I could find costs nearly double the cheapest non parity and I don't think it's worth the extra money to max out the motherboard I want to upgrade the memory on.

I'd say, use non-parity whenever the board allows it.

To me it's not an issue as I have both types of memory in enough quantity so I can basically pick whatever I want from my stack of computrash 😜
Generally older boards require parity and newer PCI 486's and above generally work just fine without parity