I am only really familiar with 3rd ed, i haven't read an adventure book. The best setting book is New Seattle.
As far as i understand each edition takes place later and later in the timeline so 1st is the 2050s and by 5th you are into the 2070s
In 3rd the first place to look is always the Core Rulebook, there is plenty in there for you to be able to use and play with. The Shadowrun Returns games are a really good place for seeing how the world is supposed to work and for ideas for playing. I would argue they are more useful than some of the published books.
There are 3 books i would look at when it comes to the setting:
The Companion Book added character creation options, advanced rules and GMing "help". The extra race options can be a useful tool for worldbuilding even if you dont want to let players use them. Edges and flaws are dangerous to include. The running the game chapters lay out types of jobs to give players and the campaign considerations are okay. There is info for including ghouls in the game or running a game where you play a gang. The flavor is nice if you want gangs or ghouls to be a big part of your world.
The solutions to common problems like "power gaming" "obnoxious characters" and "game balance" is amusing too.
The best book for information about the setting is New Seattle. The book is devoid of mechanics but is instead full of art, a detailed History chapter and information about various part of Seattle. There is stuff about Downtown Seattle the barrens the body politic, the corporate sector and the Seattle underworld. It addresses how the police respond to threats, it has a map and is written to give you different places and themes for a campaign.
Year of the Comet
The slightly controversial book that also belong here is Year of the Comet. It's a book about Haley's comet coming near earth on the anniversary of the awakening and creating all kinds of chaos. It introduces SURGE -transformations, weird magic shit, volcanoes blowing up and mass hysteria. It involves lots of big changes to the setting which isn't necessarily what you want if you are trying to get to grips with the system and the setting in the first place. I would personally pretend this book doesn't exist, but it is written to be full of adventure seeds and ideas.
I will warn you to be careful when it comes to the exact details of the setting and the world. If you try to strictly follow the world as its written in the books and find out more and more about the setting, it can be detrimental to your game in all sorts of different ways. Pick and choose what you need at remember you don't need to know it all.
You also don't need a whole lot of raw information for your campaign. For instance in the companion there is a 2 paragraphs about power struggles in the mafia and you could build a whole campaign off it. It is also written to be a seed for something, it doesn't detail the family tree or statistics and maps for the competing families but gives context and characters and agendas for you to build your own stuff around.