The games are a sequle, CDPR got the rights to make a game based on the IP in the early 2000s and just did their own thing.
W1 was a bit rough, plot wise it tried to incorporate a lot of the existing world but played the amnesia card so everyone had to explain shit to Geralt (and by extension the player).
W2 is a direct follow up to W1 and put CDPR on the world stage by being the high water mark for graphics requirements around 2010. Still a very good game, a bit on rails for modern standards, but still fantastic for how it handles branching paths.
W3 + DLC won all the awards in their respective release years for a reason, they are magnificent and with CDPR spending 15 years in the IP they make tons of call backs to the books without the players feeling like they are missing something if you didnt read them.
There are 2 (ok… 4) TV shows.
The netflix shows starring Henry Cavil, king of the nerds, (who is being recast by the least hot hemsworth because netlfix pissed off the books biggest fan) and what ever that second one was that we dont talk about (There is also an anime, which is pretty good) and the Hexer, a made-for-TV low budget show that loosly follows the plot of the early books, it in polish and I dont think it was ever dubbed (I managed to find it with subtitles years ago).
I know this is more than you asked for but, enjoy the games, enjoy the books, be aware of the fan opinions of the shows.
You could have picked any other titan from that game, and you went with the one that looks like a mushroom… (I would have gone with the Tempest, because of Clear Skies)
Also we dont have defined dates for when the game takes place. We know its atleast ~15k years in the future, but anything beyond that is fuzzy at best.