A playset of each cared is 4 of them, but a lot of the cards aren't worth having any of if you're constructing decks.
One common way to play from a set is to make a "cube", where you draft the cards like they were new packs (you open a pack, take a card, pass it, until you've gone through 3 packs per person). For that you could probably be very happy with one of each rare/mythic, two of each uncommon, and four of each common (say). Keep them sleeved up and divided into stacks by rarity - each faux pack is 1 rare, 4 uncommon, and 9 commons. You also keep a stack of basic lands for people to take from as needed to build their 40 card decks (24 cards and 16 lands).
A full set of one each of Core 221 is currently $238.74. But $100 of that is just 6cards.
Core Set 2021 MTG / MTGO Price History
The commons are essentially free if you know someone who plays though (they're left in stacks at the game shops after drafts, along with a lot of the uncommons). It looks like most of the other sets are around that too. I think that's using the median price to buy though, so you can do it for less.