There is so much reading you could do. Really, so, so, soooooo much. So you'll need to pick and choose.
For novels, yah, Hardwired (by Walter Jon Williams) is a good starting point. A couple of other classic cyberpunk novels are Neuromancer by William Gibson and Gravity Fails by George Effinger. There have also been a lot of shadowrun novels written. I've not read them myself, but apparently some are pretty good.
TV and movies tend to not do quite so pure cyberpunk, but you get some of the feel from Escape from New York, Robocop, or in a way even Aliens (no, Cyberpunk doesn't do interstellar travel, but the attitude of the corp handler is a good match, and the horror of dealing with bug spirits is somewhat akin to Aliens).
Thanks to the wayback machine, you can read an old Shadowrun primer here:
https://web.archive.org/web/20150909110710/https://s3.amazonaws.com/www.harebrained-schemes.com/wp-content/uploads/2012/04/shadowrun_primer.pdf It only goes up to game year 2062, we are currently in 2080 (maybe 2081?) The game universe advances year by year with ours, always ~61 or so years ahead of us, but the timelines diverged back around 1990 or a bit earlier.
You can also find a fairly detailed timeline on the shadowrun wiki, at:
https://shadowrun.fandom.com/wiki/Shadowrun_timeline (and of course the wiki has a lot of other info too, although it hasn't been kept particularly well up to date).
You will need other people to play with. If you don't know people who are interested, some stores and many conventions will host 'Shadowrun Missions' play. These are ~4 hour adventures that are designed to be sort of a common, shared, experience, so that you could take a character that has run in some of them in one place and play more of them somewhere else. So far those are all written for fifth edition -- the first ones using sixth edition probably won't be out until next year. So if you are interested in playing those you should looking at trying 5th.
And good luck with the amount of info out there, and have fun! (or, to use the classic shadowrun catch phrase: "Watch your back. Shoot straight. Conserve ammo. And never, ever, cut a deal with a dragon.")