@Acrylic, okay, I’m a games lunatic, and there’s a world of games out there that the “roll and move” crowd aren’t really aware of. So here you go:
Dutch Blitz- just get it. Inexpensive and way more fun than it has any right to be.
Azul- there are four versions. Look at vanilla Azul or Summer Pavilion (although Stained Glass is also very good). They are all very pretty and tactile games.
Silver and Gold- inexpensive and very chill “flip and write” (flip a card and write to fill in your spaces)
Survive!- a classic “take that” game where you can send your opponent’s little people to a watery grave. Always fun.
Qwirkle- a little like Scrabble but with shapes and colors
Camel Up- super silly camel-race gambling for 3–8 players
Sushi Go- cute card game where you pass your hand left or right
You might consider Century: Spice Road or Century: Golem Edition (same game, different art). Satisfying gameplay and turns move fast.
If you want to play 2 vs 1, Jaws (based on the movie) is very suspenseful and fun—one person is the shark, and the other 2–3 try to get the shark. Horrified is based on the Universal Studios monsters (Dracula, Frankenstein, etc.) and is fully cooperative, i.e. you three vs. the monsters.
For some nature and education, I also like TRAILS, PARKS (national parks), Wingspan (birds), and Mariposas (monarch butterfly migration).
Oh! Another good one is Tussie Mussie, which is a small card game based on Victorian flower bouquets for 2–4 players.