Here are some great games that are a good place to start. These games are quick to learn, very fun to play, and offer some wonderfully interesting decisions!
In Sushi Go!, players are trying to make the highest scoring sushi plate in front of them by playing different types of cards onto their plate from their hand. Each turn, you will select one card from your hand, and place it on your plate. Then, everyone passes their entire hand to their neighbor!
***Sushi Go Party! is an expanded version of this game, and is also excellent. It comes with many different cards you can swap out each time you play, whereas the original Sushi Go! has one fixed deck (but still provides tons of fun).
In Tsuro, players are trying to be the last dragon standing on a board of winding paths. Each turn, you will select one tile from your hand to add to your dragon's path, and then move your dragon (and any other players' dragons now connected to that tile) along the newly created path!
In Roll for It!, players are trying to match their dice to cards so they can collect them for points. Each turn, you will roll all your available dice, and then place them next to a card with a matching symbol, where they will remain until that card is completed by any player. When a player completes all symbols on a card, they collect that card, score the points on the bottom of the card, and all dice next to the card are returned to their owner. First player to 40 points wins!