All you technically need is the core Shadowrun 4th Edition rule book. After that you can get the books that expand on these rules. Those are Augmentation (for implants, medical rules, nanotech, and genetech), Street Magic (it's all in the name, this expands on magical stuff), Unwired (For all matrix/technomancer needs), and Arsenal (rules on modifying weapons, vehicles, and drones. More weapons, vehicles/drones, and gear.) Runners Companion offers a bunch of new options when it comes to life style rules, playable races, and qualities but some of the stuff should be kept from the players until they have a better gasp of the rules.
My advice is run a test campaign where you all learn the system and how you like to play it. If the players want to use stuff they couldn't before from RC then do a "retcon" of sorts where they can remake the characters a little to give them access to that stuff and play like it was always like that. Making completely new characters can be a pain after all.
Everyone should probably have at least 12 dice with them. That's not hard to find. All you need besides that are character sheets, something to keep track of information during the game, a place to play, and some willing players.