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Now, to start us off...
I like to look at the universe as a coherent whole, with an analogue scale of power ranging from "Zygote" to "Cosmic Horror," with the game taking place at some point in between.
I also believe that your position on that scale is, in fact, in character knowledge, with all the repercussions, good and bad, that that brings. People who have seen you at work know roughly how good you are, and will treat you accordingly. I build my characters, and run my games as GM, with the explicit idea that if you're not good enough to get hired you won't get hired.
I prefer Karmagen since it doesn't punish you for not being "karma efficient" with your build, letting you build a more well-rounded character while still having enough experience with their area of expertise (Sammies & Guns, Faces & Schmoozing, etc) to be considered "a cut above" compared to a standard, legally-employed professional in their field, and generally competent in their supporting skills.
I roughly define that "floor" as 10 dice on a raw, pre-equipment, Attribute + Skill pool (no specialty) for your "core" Skills, and 4-6 for your "secondary" Skills. Not a huge bar by any means.
By the same token, I also scale my OpFor the same way... "typical" gangers are going to generally be pushovers (4-5 raw dice), with guys like First Nations or The Ancients containing assets ranging from cannon fodder to Prime Runner status, while first-line "mall-cop" type security are going to be in the same boat as the low-level gangs. KE/LS forces are going to be pretty competent (6-8 "raw" dice), while SWAT / HTR forces are going to be an even match for a "bare minimum" Runner (8-10 raw). Elite commando units, of course, are going to be even higher, with guys like Ares Firewatch or S-K Prime commandos being a match for even the best-built Shadowrunner.
The key, of course, is to create jobs that match your players' strengths... people don't get hired for jobs they can't do, after all... and their place in the "pecking order."
In-game, I like tactical mission fulfillment, with enough focus on down-time to make the characters feel alive, while not dragging the pace of the adventure.
Essentially, I believe you should be making the most of what you can do versus opposition that is less skilled, but more numerous, and who has the advantage of emplaced defenses. Violence, if planned right, should always be quick, quiet, and (hopefully) on the way out and/or over before anyone can sound the alarm.
That is to say, proper planning should make the execution seem easy... barring statistically abnormal rolls... while if you screw up your prep you've potentially bought yourself a Charlie Foxtrot of epic proportions if you can't think on the fly and keep the whole Run from crashing down around your ears.
My presonal preface now for character gen is BP and chummer (chummer mainly cause it's free) I stick to the standard rules (400bp, 12 availability, etc)... and generally see the characters as "just starting out". They may have a few runs under their belts but nothing that has made a splash in the shadow community. I don't set a general threshold for competence when it comes to dice pools as my players can be a little scattered when comes to character concepts and ideas.... But I generally let them fly with their concepts and try to help them out where I can. They usually seem to end up in the 10-12 dice pool for their "main focus" skills... but their secondary can be all over the board (2 to 8 )... again, usually depending on character concept.
As for SR Canon... well, I try to keep the established histroy as canon... then work from there, imposing sound bits of changes tot he world as they happen (even if they played no part in it) and change the world as the players interact with it. Generally speaking, I don't let my players stray too far into the "great white beyond"... so even if they try to plan the "great assassination of Damien Knight", they generally will not have the opportunity to do so (but I don't stop them from planning it out... or even trying to execute their plans... they just have a much higher chance to fail)
As for the power of the game, I take a more economical approach to things. Gangers and other lowlives are at the bottom and will have a dice pool of anywhere from 4 to 14. 4 being the no-name ganger kids that occupy a 4 bloock hood, adn 14 being the top line Cutters, ancients and other major gangland players. Organized criminals like the Yakuza, Vory, and Mafia ruin at a different scale and may (or may not) have combat ware... depending on their roles and level in the organization.
As for law enforcement and secuirty, these will be trained and skilled individuals, with good personal equipment, but I just don't see (personally) corps spending tens of thousands of neuyen to outfit what essentually boils down to 'front line support staff' having alot of combat ware. So whiel a smartlinks my be the norm, initiative enhancers are not. combat drones however, are something I make use of more often (again they just make more economical sense to me. No cyber/bio ethical issues, no death payouts, no hazzard pay, no medical bills for injuried employees, less mental trauma, etc, etc, etc.) However, as you get into the HTR, SWAT, firewatch teams, and black ops operatives, you see progressively more and more combat ware come in to play.
I too try to match my player's skills and characters to the "jobs/runs" I offer them, with pay being reflexed with how successful they have been in the past, other factors. I occasionally take them out of "their comfort zones" to shake things up a bit, and introduce them to the "wide, wide world of Shadowrun" but these are usually small time affairs that don't stray too far from their bread and butter roles. Generally speaking this has fustrated my players as they express interest in "expanding their horizons"... but when I allow them to, they have often found out they are not quite ready for it... yet... (like being combat builds that want to do stealth missions... with a 4 infiltration...or dectective work.. and defaulting on intelligence gathering skills)
As for what type of game "style", well I let the players dictate that as much as I can (combat heavy or light, RP heavy or lite, etc) but I do pay attention to "response zones" so while having a running fire fight with gangers int eh barrens MIGHT get a police response in, 2 or 3 HOURS, a battle in the downtown core of a city will see a response time measured in minutes (with more backup and drones mintues behind the first responders, and HTR mintues behind that) in short, I try for a realistic feel (as realistic as you can get for a future sci-fi based game anyways)
I try to plan out static emplacements of barriers and patrols of mission sights in advance (as well as spirits, drones, biologicals0 so I have this info ready for a good gather intel roll, and to avoid GM meta-gaming over a brillant plan by the team. (if they can figure out a way to bypass what I planned, GO TEAM!) but I do leave a few random things to chance (nothign ever goes entirely as planned
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I try to make allowance for "Player Ego" but then again, sometimes their egos are a little to big and they earn a swat on the butt. (you REALLY want to spit in the oyabun's sake?? REALLY??? Ooookaaayyyy <wince>.)
I also place a general limit on just what my players can find on teh markets depending on the areas they are playing in (No heavy Milspec armor or Gauss rifles as my last party found out) This is usually to avoid future problems that come from what I precieve has 'eqiupment power creep' which I have to address by thus deploying larger return firepower. After all, if a partry of military specc'd terrorists attacked a city, it wouldn't the police that responded... but the military! Conversly, I don't make general deployment of such gear and firepower against the characters either.. unless it is as RP showpieces ("you get waved through the NAN checkpoint by the guard wear medium milspec armor, on the fortified tower turret, you watch the Thunderstruck gauss rifle target the next car in line....")