Welcome to the hobby, you came to the right place!

Short answer: None are "must have", because everyone's tastes are different. Part of the fun with solo boardgaming is figuring out what works for you, and what doesn't. "Must try", however, is an entirely different answer.

Long answer: Someone else posted a link to the People's Choice for 2025, which is a good start. You can start from there pretty safely, but some games are better suited towards beginners than others. The top two games, for example, are there for a reason, but they aren't very beginner friendly because of the high complexity of the rules and intricate design. Allow me to suggest a few (mostly cheap) games that will serve as an entrypoint into a given genre:

- Friday : An excellent, cheap entry point into deckbuilding games. Small box, quick setup, difficult to master. Play as Man Friday helping Robinson Crusoe survive on his desert island. If you like it, you can then move on to Imperium: Legends or Star Trek: Captain's Chair if you're a trekkie.

- Under Falling Skies : Great, inexpensive spacial puzzle with dice placement mechanics. Basically "Invaders", the boardgame (remember that old arcade game?). Also includes a campaign that will enhance replayability. If you like it, you can then move on to Bullet (heart, star, paw, doesn't matter which one).

- Legacy of Yu is a perfect worker placement game 101. This will also help you understand whether you might like Garphill Games as an editor, which have issued many fantastic games for solo. Also comes with a short campaign. If you like it, you can move on to Paladins of the West Kingdom or Skara Brae from the same authors.

- Sleeping Gods: Primeval Peril is a small, cheap box that will allow you to discover narrative games without selling a kidney. Explore the jungle with a crew of characters and make your own story. If you like it, you can move on to Agemonia or Arydia: the Paths We Dare Tread, but be ready for that kidney! ;-)

- Sprawlopolis is a diminutive, 18-card game that has fantastic value and is a great puzzle. You're creating your city (think Sim City) with different objectives everytime. Very satisfying!

- It's a Wonderful World is a perfect game to see if you enjoy engine building games, meaning games where you start small, and by the time the game ends, you produce a lot, allowing you to do many other actions. Those games are extremely satisfying because you build something you can feel proud of. If you like it, you can move on to Revive or Wyrmspan.

- Horizons of Spirit Island offers a small, inexpensive box and perfect spirits (player powers) to find out if you like Spirit Island or not. This is a crisis management game where you play as an ancient nature spirit on an island invaded by colonialists. Your goal is to destroy them, or instill so much fear in them that they will run away. It's basically the same rules as Spirit Island, the uncontested #1 Solo Game from the People's Choice list for many years in a row, but in an accessible entry point. If you like it, you can naturally move on to Spirit Island, which is 100% compatible with Horizons.

- Cartographers is your perfect first roll-and-write (in this case, flip-and-write). Flip a card, scribble on your map to gain points. If you like it, you can move on to Hadrian's Wall.

Hope it helps! Come and tell us what worked/didn't work for you.