I would try to cover a wide range of heaviness and playtimes. Fuck theme. I would prefer to have different genres, but don't mind an overlap if they are of different heaviness and playtime.
My 10 games would be:
A deck of cards. Preferably a nice full tarot. Cheating, yes. But by the fact that most people are familiar with a deck, and the great variety possible, it's impossible not to include. Also, Screw, Conquian, Texas Hold'm, Hearts, and my homeruled version of War are each good enough games to be included on their own. You can use a deck to play stuff like Mafia, Skull, Sushi Go, or any other simple game.
#2 - Cacassone. A classic for a reason. Simple enough to teach to toddlers and geriatrics, complex enough to have real strategy and replayability.
#3 - Agricola - Preferably with curated occupation and improvement decks. This game is great. I don't know what else to say.
#4 - Hive - Deceptively simple, great clean design. Take it anywhere and play. I'd rather include this than chess, backgammon, or any of the old classics.
#5 - An MTG custom gauntlet. A carefully designed set of decks (anywhere between 6 and 12 unique decks w/ sideboards) that have been balanced against each other. Format agnostic. Full of custom cards to make shit work. Been meaning to build this IRL.
#6 - Kingdom Builder. I just played this recently and already it's become one of my favorites. Again, simplicity and clean design create interesting strategic depth without bogging shit down with rules or phases.
#7 - Chinatown - Takes the classic bartering that people love from Monopoly and Catan, and turns it into a decent game finally.
#8 - Codenames - Feel free to include your favorite party game here, but this one feels the most clever and strategic while remaining fun. Just make sure to use a timer.
#9 - Heroscape - I have a soft spot for this, and it fills the wargaming niche. What a fucking great game.
#10 - Battleball - Fuck yea.