I wouldn't jsut limit myself to SR3. I would go back to SR1 & SR2 as well. Shadowrun has been one of the most consistently "quality" roleplaying games I have ever seen. The 95% of the fluff is completely applicable to SR4, IMO. I am trying to think of an old book that is an utter dog off the top of my head and nothing is jumping to mind.
I would say any of the location source books are important to have. It's hard to say what you will find relevant, tho', without knowing more about your game. Assuming you are running a traditional game set in Seattle or the UCAS or Denver, I'll list what I think you should have. I will try to rate them on a 5 star scale and make a quick note. they are in no particular order, either quality or chronological, other than being subdivided into Location, Organization or Miscellaneous. I also included Ebay listings (not mine!) of everything I could find that was one my list.
Here ya go:
________________________________
LOCATION BOOKSSeatle Source Book (SR1) 4.5/5
Ebay ListingExcellent book to own. Damn near indispensable if you are running Seattle.
New Seattle (SR3) 4/5
Excellent book to own. Indispensable to a Seattle setting. And the cool thing? It's full of info, but has little redundancy with the original Seattle Source Book. The writers did a great job. All setting books should be so good.
Denver-City of Shadows (Boxed Set) (SR2) 4.5/5
Are you running SR4? Are you set in the new default setting? You HAVE to own this. People's feelings vary about this setting: Some find it unreal, others think it's awesome. I happen to be in the latter group. No one that wants to run anything in Denver will probably tell you it's anything but indispensable, even tho' Ghosty comes in and changes a ton of stuff after it's writing. (Written by Nigel Findley, for those who care about that sorta thing.)
Native American Nations:
Vol. 1 & 2 (SR1) 3.5/5
In the first two editions the injuns were a LOT more important to the game setting. SR3 got away from that a bit and SR4 seems to damn near ignore them. Too bad, cause they were fun and interesting. Also, they are a HUGE influence on the Denver setting. Each book includes a scenario to run as well. (Written by Nigel Findley)
Target UCAS (SR2) 3/5
Important and useful, but I always found it a hard read for some reason. Covers Chicago (post Bug City), Boston and Detroit
Bug City (SR2) 4/5
Run a whole campaign here! Very good book on the bug takeover of Chicago.
Target: Smuggler Havens (SR2) 3/5
Covers New Orleans and Vladivostock and other smuggling places and things.
Atzlan (SR2) 4/5
Find out jsut why everyone hates those damn Atzlaners. Have yourself a Cinco de Mayo run! Drink Corona. (Written by Nigel Findley)
California Free State (SR2) 2.5/5
It's important if you are playing on the UCAS continent (tho' it's not actually UCAS), I never really liked the book.
Tir Taingire (SR2) 3.5/5
You
have to own this. I mean, come on, those wacky elves are about a fifth of Shadowrun and this is the closest enclave to Seattle or Denver. It's pretty well done, as well, even if the culture doesn't make complete sense.
Tir Na Nog (SR2) 3/5
Important elf book, but I found it... clumsy and not as well put together.
Year of the Comet (SR3) 3.5/5
Huge update for all over the place of the SR world including California, Atzlan, Japan, Denver, Introduces SURGE and Ghostwalker and so much more.
Shadows of North America (SR3) 3.5/5
Covers and updates the Algonkians, Denver, California, the CAS, Quebec, Salish Shidhe, the Sioux Nation, Tir Tairngire, UCAS and the Utes.
Target: Awakened Lands (SR3) 3.5/5
Covers Australia and a lot of magical locations like the Bermuda Triangle, Crater Lake and Mount Kilamanjaro. Like most of the later SR3 stuff, it's solid but seems to lack a little something somewhere.
ORGANIZATION BOOKSUnderworld Source Book (SR2) 4.5/5
Ebay ListingGreat for almost any GM. No matter where you go, there's gonna be organized crime. The book goes into good detail. Really, full of great fluff.
Lone Star (SR2) 3.5/5
Who doesn't wanna know about the natural enemy to Runners? Even if Lonestar isn't the local police, you'd better believe they are security somewhere in your setting. Also a good template to model other security companies on. (Written by Nigel Findley)
Corporate Download (SR2) 4/5
Indispensable if you wanna use corps in your game. Period.
Portfolio of a Dragon: Dunklezahn's Secrets (SR2) 3.5/5
The dragon has been dead for 13 years and he STILL makes ripples in the Shadows. If you want to know about ol Dunky, this is the book.
Dragons of the Sixth World (SR3) 4/5
I's about the DRAGONS!!! What do you think? *L*
MISCELLANEOUS BOOKS (Un-categorical)
Paradise Lost (adventure/location source book) (SR2) 4.5/5
If only there had been more books like this. Technically labled an
adventure, the back half of the book is actually the source book for Hawai'i. It manages both things marvelously. I highly recommend it. Besides, think how happy your Runners will be when they win that vacation to Hawai'i

(Written by Nigel Findley)
Cyberpirates (SR2) 3/5
Part organization book, part setting book (The Caribbean League) it's worth having in your collection if you want to know about that part of the world. Personally, I felt the whole "pirates" thing was a little over the top, tho. Still good info and an enjoyable read.
Renraku Arcology Shutdown (adventure) (SR2) 4/5
Far more than your typical adventure,
RAS is darn near a setting/campaign all of it's own. You want to do something with those huge honking too powerful PCs? Challenge them, get them out of your hair? Throw them in this nightmare world. Or, create characters especially for it and run it for a change of pace. It's the closest thing to a "Ravenloft" that Shadowrun has. Truly enjoyable.
Universal Brotherhood (adventure/sourcebook) (SR1) 4/5
More bugs! If you liked Bug City, then this is where it all began. (Written by Nigel Findley)
Critters (included with the SR3 GM screen) (SR3) 4/5
Ebay ListingUntil SR4 comes out with a Paranormal animals version, this is the best thing to get. Sure, you have to buy it with the now useless SR3 GM screen, but seriously, it's worth it. It's not overly expensive at 10-12 bucks (or less used), and it descibes a LOT of different types of critters. Come on, PC's need more than gangers to whoop on.
________________________________
Finally, I will try to list the above books really important to different settings. There will be duplications:
Denver:Denver: City of Shadows
Native American Nations-Vol 1
Atzlan
Shadows of North America
Year of the Comet
Corporate Download
Underworld Source Book
Critters
Seattle:
Seattle Source book
New Seattle
Shadows of North America
California Free State
Native American Nations-Vol 1&2
Tir Taingire
Renraku Arcology Shutdown
Corporate Download
Underworld Source Book
Critters
Year of the Comet
________________________________
So, I hope that helps you out!
Vlad