The Kester #44 60/40 0.031” Lermod linked is all you really need for pinball or anything else, and a pound will last forever. (I think you can generally ignore exp. dates if you store the roll in reasonably stable conditions - I have some Multicore 63/37 from the 70s that’s still perfectly good!)
Although they claim it isn’t strictly necessary, I still like to clean the flux residue as thoroughly as possible using either 99% “technical grade” IPA or Techspray Flux Remover.
Regarding 63/37 vs. 60/40 alloys, I was once told by an engineer in audio electronics:
63/37 wets, flows, and solidifies quicker and is good for PCBs and delicate situations where you strongly prioritize minimization of time heat is applied.
60/40 forms stronger and more pliable joints and is preferable for heavier gauge wire, terminal lugs, and point-to-point connections. It also works fine for PCBs and is the best choice if you want a single “all-purpose” roll of solder, it’s just possibly slightly less forgiving of suboptimal soldering technique.
In my experience, Kester #44 62/36/2 (2% Ag) is the easiest to work with of them all (I like it for SMD) and makes connections that sparkle like jewels, but it’s expensive and technically unnecessary unless you are soldering silver-bearing wire or components.
