As a Shadowrun player and GM from the beginning (yes, the 1989 beginning, pesky whipper-snappers!), I'd have to say that everyone's advice here is rock solid. Especially the bit about mini-runs (I'll second that "here, here" with a +1 rep, my good man). I would also like to repeat what was said earlier about glass cannons, and help a bit with bringing your players in from different systems.
For players used to D&D style gaming, there can be a significant disconnect when actual combat happens. This happened in the most recent game I ran, so I'll share this concrete example. One of the players was running a street samurai (think heavily cybered/augmented combat monsters). On the first round of the first combat the team encountered, the sam stood out in the open taking shots at the enemy, not bothering to go to cover like the rest of his team. He wounded one of the opponents (who had dived into cover, himself) but was nearly made into street pizza by the resulting return fire from a SINGLE member of the opposition. He almost died, actually, and was only saved by his armor, use of edge to reroll failed dice, and lucky die rolls. By straight odds, even with edge use, he should have been dead.
The following action, the sam crawled to the safety of cover.
The next thing I'll cover is setting. There is a big difference between the have-not's (anyone SIN-less, like the PC's) and the have's. The have's live in neon colored, nigh pristine, ultra Big-Brothered areas living lives of endless consumerism. The have-not's have no right to even drink the water or breath the air, according to the authorities. Without a SIN you can't legally go shopping, or even ride a bus. Basic services (water, electricity, sanitation) are sometimes provided, but without legal rights to fair treatment, the SIN-less often get shoddy service on top of outrageous prices.
Really play up the difference between having it all and having nothing. The reason there's no open civil war is, well, because no one cares enough to fight you. Apathy is the watchword.
To finish up I'll list some books, films, or TV shows that highlight either the setting or the way the runners typically do their runs.
Burn Notice (TV): Excellent show about a clandestine team of capable individuals living outside the law. Super Bonus: it has Bruce Campbell in it.
Leverage (TV): Another exellent show that highlights the different roles used to perform ops outside of the law.
Blade Runner (film): Everything cyberpunk seems to take its visual cues from this film (and with good reason). Excellent film, especially the Final Cut.
Ronin (film): This movie seems to not realize that its about a group of Shadowrunners, since it's set in modern day Europe. Great De Niro film.
Neuromancer (book): By William Gibson, who actually doesn't like Shadowrun that much. Excellent read.
Snow Crash (book): By Neal Stephenson. Great book. No augmented street sams, but heavy use of the matrix and hyper-capitalism themes. Great stuff.
That's all I got off the top of my head. Good runs and have fun!