For Sourcebooks, it really depends on the make-up of your group, and their preferences and knowledge of Shadowrun.
Arsenal is highly suggested by me for any group. The gear in that can be used by any character creation from Mundane Hobo With A Shotgun to Magician In A High Lifestyle and everything in between. I would also highly suggest "This Old Drone" E-Book to support this, as it has drones useful for GMs and PCs in it. MilSpecTech less so, unless your group is threatening to steal Fighter Jets or something... The new Unfriendly Skies would be a better suggestion to MST.
For experienced players (Even if they don't know Shadowrun), I also suggest Runner's Companion, which has extra character creation rules, and the Advanced Lifestyle breathes a lot of life into a major and important part of the character's life.
Augmentation is useful with the cybernetics and bioware crowd, and even the information on medical services can be found useful. May not be an immediate purchase, but one of the top for sure.
If you have a player(s) who love magic, Street Magic is a good buy. It was the only other 4th Edition for the longest time. But if you don't have any interest in magic of magicians, it can be left by the wayside. "Way Of The Adept" gives Adepts some love they've been desperately been needing, and is suggestible if you have one in the group.
Unwired is useful if you want complex Matrix Rules, but is really rules intensive and wordy. Not one I'd suggest for a new group, but maybe a digital copy.
For Fluff Books: Attitude, Vice, 6th World Almanac, and Spy Games, in that order. Perfect for groups that don't know the universe that well, or even experts in it. Not much in the way of "Crunch" in those books, but a lot of stuff that can be used to flesh out scenes or characters! (I'd rate Spy Games higher if the Crunch in it was fixed.).
If you're a GM that likes critters, Running Wild is a must, with the Parazoology E-Book supporting it.
I cannot suggest War! at all.
Now, depending on what city you're running the game in, the splat books for the various areas are decent enough, but lacking the info needed from a full supplement. If you're running in Seattle, then Seattle 2072 is a must-buy. If your group is in Denver, then Spy Games moves up on the purchase list as it's got a great write-up in it that fills in a lot of details we haven't heard about since the OOP Denver Box Set.
Hope that helps.