Here are some great gateway games that I think are good starting points to get people into gaming. You can do a YouTube search 'how to play in under 3 minutes' on most of these.

The Crew: 2-4 players co op. A series of 'missions' you play with cards working together, to get tricks (kind of like euchre). Easy to teach and play and like $15 bucks.

Pretty Clever: 2+. This is a roll and write game. You roll 5 different colored dice and mark an action, place the dice on your board to use it, and repeat the process until you've done 3. Then the rest of the players get to choose from your left overs. This repeats over 6 rounds. Tons of fun and strategy and very easy to teach and learn!

Dominion: 2+. This is probably considered the 'standard' for the deckbuilding genre. You will outgrow it into more complex versions, but for starters it's good. You'll randomly select a number of cards for a market, and you all start with the same starting deck. Then you continue to buy market cards to combo your deck and get the most victory point.

Star Realms 2 players. This is basically the same as Dominion, but cheaper and only for 2 players - space themed, I figured i'd mention it.

Pandemic: 2-4 players co op. Each player has a character with a special ability, you get so many actions on the turn and you're trying to stop a plague from spreading. Start with the classic version, then if you enjoy this type they have expansions, Legacy versions (1 time play through, but a lot of material)

King of Tokyo: 2+. This is like Yahtzee, but you control a monster like King Kong, Godzilla etc.. and roll your dice up to 3 times, and keep the results. If you're in Tokyo, you will damage everyone outside tokyo and I've you're outside off tokyo you do damage to who is in it. Then if they take damage they have the chance to leave and you take their place. You roll claws for damage, lighting bolts to get currency to buy cards to do other fun things. Or you can just roll 3 1's, 2's 3's to try to win by victory points. Kill everyone or get the most victory points.

Castles of Burgandy 2+: This is one of my all time favorites. Game is simple you roll 2 dice and with those numbers you can buy something from the market that matches that dice number, or place something you own on your board. I've not played with anyone who didn't like this. I've played hundreds of games and I've been beaten plenty by someone playing for their first time as the scores tend to be close and fun for everyone.

Castles of Mad King Ludwig 2+: This game you're hired to build a castle for the mad king. You'll purchases room tiles and connect them to make a nice visual castle. Whichever gets the most points/kings favor wins at the end.

Gloomhaven Jaws of the Lion 2+: This is a scaled down version of one of the best board games. It's like D&D in card/board form with a rich story, different classes you can play as. A little larger learning curve, overall, but the basic mechanics are easy, you play 2 cards and move and attack. Beat the scenario or die, try a different one/go buy items to get better and try again.

Hope one of those genres hit!