I'll answer the second question first. I hate the video game because it's not Shadowrun, yet they slapped the name on it, tried to pretend it was Shadowrun, and showed who knows how many people a POS game that's nothing like the real SR. It could have stirred interest in the actual SR game. Instead, it made a lot of people think that this is what SR was supposed to be. I'd have felt the same if they'd done it to, say, D&D, or Deadlands. It might be a decent game on it's own - but it should have been called something else. If they want to make a SR game, they need to make an SR game, not a subpar FPS (which it really was) with a brand label slapped on it.
Now for the first question. SR groups are extremely flexible, really - a good thing, since it's classless and everyone can make whatever they want. There's basic roles, really, but no one needs to be constrained to them. Street Samurai are your basic tough guys (no code of honor, usually, despite the name). They're typically the guy with so much cyberware they're nearly a cyborg, often good at close range combat, typically with some melee, though they often favor the big damn honkin' guns, too. You've got your infiltrator, who's the sneaky SOB that God himself couldn't see. Ex-ganger (or maybe not so 'ex') who favors concealable weapons, often has claws, and tends to be flamboyant as all hell. Your 'face' type characters, who are the ones who can negotiate extremely well, tend to have a lot of contacts, and often aren't the best at combat. Then, of course, there's mages and shamans, the primary magic-types in SR. Mages take the 'scientific' approach to magic, while shamans take the naturalistic approach (and often have a mentor spirit). Adepts use magic to enhance their bodies and capabilities, while mages and shamans use actual spells (everything from healing to making things go boom.) There's a lot of other possibilities, too, like snipers, straight out thieves, assassins, whatever. If it might fit into a criminal world, there's a chance it'll work in SR. A good group often has (But it is no way required) a front-line type (like a Street Sam, who can take the attention), a face, a mage of some sort, an infiltrator. But I've seen groups do very, very well missing several of the above types, and be none the worse off for it.
It's also worth noting that in SR, you're often not really a 'party' like you might think of in the D&D sense. You could be an entire group of freelancers, brought together for a job by your employer (Mr Johnson - always Mr Johnson). Or hell, I've even seen groups where everyone's working at cross-purposes.