To resolve combat in Gary Gygax's Chainmail and the original edition of D&D, you rolled two six-sided dice. d20 was an optional addition. Six-sided dice are ubiquitous. It's no surprise Gygax employed them. So why did players come to prefer all these funny dice?
There are a few ways to think about what dice to use for a game.
The Dice are Made Up and They Don't Matter
As long as you have randomizer, you have a game, right? You could use dice, cards, an app, coins, or an overly elaborate but shoddy spinning wheel. Maybe it doesn't even matter how often a player gets a good result.
This carefree approach will save you some time. You can copy an existing one or make a slight alteration.
The Dice Make the Game
Despite the original d6 system, D&D is a d20 system now. The two are linked in everyone's minds. Call of Cthulhu is two d10s. Shadowrun is d6s. World of Darkness is d10s. Genesys is ???. Unless you create your own dice (please don't), you will have to use dice that are already associated with another game. The only question is how much you deviate, how much you try to innovate.
Keep it simple, right? Don't try to reinvent the wheel.