The most common mistake in buying a chip set is buying a set. A boxed 500-chip set decides your denominations for you, and it is almost always wrong for the game you actually run — too many high values, never enough of the one you bet with.
Tell it how many players and what they are buying in for. It gives you a starting stack that makes change properly, and the totals to order.
Fewer than twenty and players cannot make a meaningful bet without breaking a big chip every hand. Many more than thirty and the stacks become slow to count and awkward to push. Twenty to thirty is where a stack is readable at a glance across the table.
Almost every set runs out of the lowest chip first, because that is the one the blinds and the small bets are made in. If you are going to over-order one denomination, order that one.
A game where everyone can rebuy once needs roughly twice the chips, or a colour-up halfway through that nobody enjoys. Decide before you order, not at midnight.
Around 200 for a $20 buy-in with no rebuys, and about 400 if everyone can rebuy once. The calculator splits that across denominations for you.
Three is enough for a home game: a unit chip, a five, and a twenty-five. A fourth only earns its place when the buy-in is deep enough that stacks become unwieldy.
Only if its breakdown happens to match your game. Most boxed sets are heavy on high denominations that a $20 buy-in never puts in play.