Important differences between the SR setting and real life :
-Magic.
The Awakening is the key difference between SR and our world.
Not only because some people can do otherwise impossible and downright scary things, but because UGE, goblinization and SURGE have lead to humans making up only 68% of the worldwide population.
-Advanced technology.
Cyberware and other augmentations are everywhere, especially among the upper class in the sprawls.
Unaugmented people are at an increasing disadvantage, as everybody who has enough

can get 'ware to become smarter, stronger and just plain better than them.
Besides that, it is technologically not so terribly different from today.
Just imagine that everyone is online all the time and what this entails.
Not that hard to imagine.
Besides the fact that the matrix is...coming alive.
There's 250.000 AIs worldwide, then there's the whole technomancer and sprite thing...it's a wild, unsafe place full of insane possibilities and things beyond the grasp of Joe Average on the street.
-Corporations that act like sovereign states, locked constantly in low-intensity warfare against each other.
The Big 10 are the real superpowers in the world of SR.
They make their own laws, they've got their own armies (including even nuclear arsenals), they controll the economy, they are the ones who really pull the strings.
-Failing nation states and balcanization have become the norm even among first-world-countries.
This adds to the importance of corporations, who take over more and more traditional duties of nation states.
Police forces are privatized in most major sprawls, Horizon has just bought the public school systzem and so on.
As far as books are concerned, Augmentation is my favourite, even though i mostly play unaugmented mages.
It's the best of the core rulebooks IMHO, but there's also a lot of fun stuff in Street Magic.
But if you want to encourage your players to stat up some mundane characters, Augmentation might be the better choice.
Unwired is also very useful for integrating the matrix into your game.
Arsenal will be easy to incorporate into a running campaign, a lot of the gear in it is cheap anough to be picked up whenever the players want to.
Runner's Companion is interesting, but everyone will want to make new characters after you've bought it, so it may be a good purchase before you want to start a new campaign.
It also has a tendency to being the most unbalanced of all core rulebooks, containing some extremely good options as well as extremely underpowered ones.