So with our skepticism suspended and an open mind, let's get started.
Steam
Most of the titles I'll be listing here can be found on Steam, currently the world's biggest and most accessible PC gaming platform. You can make an account for free, the client runs fairly light-weight and boasts a ton of useful features for building and managing a game library and social interaction. In particular, the Family Share and Remote Play Together features have never made it easier to freely share titles between family members and stay connected with them.
Strategy
Civilization 5- one of the classics of the genre, Civilization tasks you with taking command one of several real-world nations and building it up from the literal Stone Age: establishing cities, expanding its borders, researching new technologies like Writing and Gunpowder and managing its economic and cultural development, all through the course of history up to the modern era, where your ultimate goal will be to find some way for your nation to stand "the test of time". Will that be through warfrare, conquering your neighbors? Technological advancement, being the first nation to colonize another planet? Or cultural impact, ensuring that history will never forget the people who shaped societies worldwide? The choices are entirely up to you. Multiplayer
X-COM: Enemy Unknown- coming from the same developers as the above-mentioned, X-COM takes a more personal scope, putting you in command of an international military organization charged with fighting off an alien invasion. The game is divided up into two phases: you'll first manage X-COM headquarters, recruiting new soldiers, building new facilities and constructing new gear, but when the aliens strike, you'll need to decide where to send your strike team and command them in battle, making full use of the environment and their abilities to overcome a technologically-superior foe. Challenging but rewarding, X-COM lets you tell your own story of triumphing over impossible odds. If it hooks you, there's also a sequel to sink your teeth into.
Stellaris- Taking the scope in the opposite direction, Stellaris is much like Civilization but on a galactic scale, charging you with managing a nation that has just achieved space flight. While exceptionally complex, Stellaris is rewarding in the depth of its spontaneous storytelling, with hundreds of different events and scenarios for you to encounter as your people explore the stars. Multiplayer
FTL- But let's say you like the exploration of space travel but want the more personal scale of X-COM? FTL has you covered. Taking command of a starship on a mission to get back home before an enemy fleet catches up, FTL is a rogue-like where every journey is randomly-generated. Coordinate your crew, manage ship systems and power distribution, encounter scenarios offering difficult choices and fend off hostile ships as you travel through the galaxy to reach your destination. Ever wanted to be a Captain in Starfleet? Now's your chance.
Darkest Dungeon- If you're looking for strategy with more of a gothic horror vibe, Darkest Dungeon presents one of the most nightmarishly atmospheric settings around. Tasked with seeking the source of a corruption that has gripped your family's old estate, you must hire, guide and manage teams of adventurers on expeditions into the ruined halls, overgrown forests and underwater caves of the surrounding countryside. Though challenging and unsettling, Darkest Dungeon offers a deep experience like few others.
Oxygen Not Included- But maybe you want something a little more laid-back that teaches you a bit about science to boot? Oxygen Not Included is a sandbox title similar to Sim City where you control the foundation and maintenance of a space colony. The developers have gone to staggering lengths to accurately simulate the physics of liquids, gasses and heat, offering creative problems with equally creative solutions and the cavernous depths of details you'll need to consider, everything from how to lay down plumbing for a bathroom to what material to make the pipes out of and what temperature the liquids you pump through them should be. At least the light-hearted, cartoony visuals keep things from getting too serious.
Action
Bioshock- Far beneath the ocean lies the city of Rapture, a capitalist's paradise, but one that lies in ruins by the time you arrive. What happened in this impossibly imaginative metropolis? How was it created, and how did it all come crashing down? That is the mystery you set out to uncover when you step into Bioshock, a story pieced together bit by bit as you explore its flooded districts, collect audio logs from its residents and fend off the mutated survivors. It's hard to say much more without spoiling the surprises this title has in store, so would you kindly give it a try? If you enjoy it, it's got two sequels that are equally worth your time.
Half-Life 2- In a similar vein, Half-Life 2 tasks you with navigating the perils of a world in the grip of alien occupation, its tale largely encompassing the twists, turns and trials of your journey, from a city under martial law into the tunnels beneath it and the ruined countryside beyond. Half-Life is particularly noteworthy for its focus on physics and solving puzzles centered around it; at one point, you receive a Gravity Gun that allows you to pick and toss around objects, allowing you to manipulate the world around you to open up new paths and overcome obstacles with creative solutions. Do note that this is a sequel, but I have never played the first one myself and I was able to get a handle on what was going on quickly enough.
Portal- Maybe you like the idea of physics puzzles and creative solutions but want a slightly less dystopian setting? Portal's got you covered. Handing you a Portal Gun that allows you to place two rifts in space on any compatible surface, you are then ushered through a series of test chambers where you must use your new tools abilities to bend the laws of physics to reach the exit. A simple but delightful little title made all the more enjoyable by the snarky, deadpan AI overseeing your journey. Has a sequel with Multiplayer.
The Mass Effect Trilogy- Some of the finest storytelling in gaming, the Mass Effect series is a role-playing space opera adventure where you take the role of Commander Shepard, the first man (or woman) chosen to join the galaxy's elite peacekeeping force and tasked with uncovering a conspiracy that could threaten the entire universe. Along the way, you'll have to make decisions great and small, from how you approach a conversation to whether you show mercy to a defeated enemy, with every decision having potentially wide-reaching consequences. Featuring a setting blending some of the best elements of Star Wars and Star Trek, Mass Effect's plotlines and cast of characters will have more an emotional and philosophical impact on you than you might expect. The third game in the series has Multiplayer.
Dragon Age- By the same developers of the above, Dragon Age features a similar formula but in a fantasy setting: the decisions you make will have lasting effects on the world and its characters, shaping a story both written by its creators but also more personal to you who ventures into it.