I'm somewhat surprised I haven't found this and I wouldn't be surprised if it has been asked before, but is there any inspiration behind the design of the Poke Ball? Or is there no symbolism whatsoever?
Poké Balls are inspired by the capsules for gashapon machines, which contain small, handheld toys.
Source
So, according to Bulbapedia, Pokeballs are based off of capsules for toys. As for what a gashapon machine is, this is the wiki article linked on Bulbapedia.
Hope this helps! :)