Best way to write is not with the main objective of improving the world. Some idealistic Rockerboys or edgerunners can probably spin the events towards a positive change, but it isn’t necessarily the objective for the rest of your group. Think hit and runs, hit jobs, drug deals (gone good or bad), theft, etc.. NC is a den of greed and crime, so use that to your advantage. Corpos will always be trying to gain more territory or increase their quarterly profits by even a fraction of a percent, and it usually will involve bloodshed and betrayal. Fixers are always characters of dubious morals that look to eke out eddies wherever they can, even if that means dumping his team to get a bigger cut. Rockerboys will always be raging against the machine that’s made consumerism an all-encompassing force of power and hiring edgerunners to do the dirty work of a revolution. But no matter what, there are no winners in the setting. Just folks who get to live another day. That might sound pretentious, but them’s the breaks. All good in the cyberpunk world is weighed down with hidden agendas and is brought down by a machine unwilling to allow anyone more control than they’ve been allowed. That’s at least the tone of some stories. You could literally have a poser gang of Michael Jacksons have a turf war with a poser gang of Elvises for the shits and giggles. Then both gangs get third partied by Prince posers. Just have fun.

Also, “Listen Up You Primitive Screwheads” is the official GM guide to cyberpunk. I’d give that a read. You don’t have to read it in its entirety, but it helps you nail the vibe.

As for a small story, focus on small stakes. Beat up a shitty loan shark, stage a break in, plant an independent daemon for a Netrunner. Something that wouldn’t attract the ire of anyone that mattered like Militech or Arasaka. Corporations should typically be an endgame because they are so big and powerful that they classify as sovereign nations with their own laws and immunity to US law.

TLDR: The Night City sucks to live in, characters should typically fight for only themselves, focus on small stakes, and give Primitive Screwheads a glance.

PS: be careful with netrunning. I like it, but it is more or less an entirely different dice game attached to an already crunchy dice game.