Zero Escape: God, I love this series so much. The puzzles are interesting and challenging, the characters are actually intriguing, and the story just straight up rocks!
Gears of War: The 4th and 5th games are hot garbage, but the original trilogy is amazing, one of the greatest trilogies of all time. The characters were memorable, the story was amazing (you will have to read the comics to understand some things fully, but they aren't absolutely necessary, the comics are great though), the online multiplayer gave me some of the best gaming memories, and the music is great. If you want to play these games, definitely play the original trilogy first, they are old, and the online is dying, but they will give you some great memories.
Street Fighter: Another game series that gave me some great memories. This is a very complicated fighting game, but if you learn it, it's absolutely addicting.
Fallout: Played every single game more than 10 times already. The stories are absolutely amazing. The lore is intriguing. The characters are memorable and lovable. Try these games out when you can.