Shorter version / TL;DR: I prefer to keep it in-lore and humble (no 'snowflake'), my char likely has a brief (given the age) cop and corpo background and decides to move to Night City with a clean slate for better opportunities compared to the potential dead end they think they would've reached in that other city or place they come from. Due to the background, they will likely look favorably upon certain corporations and maybe (parts?) of city police as relatable colleagues and at least not look actively for trouble or have an anti-attitude unless provoked by the other side or given the circumstances of jobs they can't refuse, or don't want to refuse.
Slightly longer: While you specifically mention portraying other characters from other settings, this post might be a bit seamless and picking up other topics on the side.
I usually like to keep it "in-lore" with character ideas or backgrounds. For me it is the most fun and not tugging at immersion.
Before we got solid information about the game protagonist and rough plot in 2018 and onwards, (the way I recall it) many assumed you'd probably be able to pick a faction and role or job more freely. My initial idea was to play a cop or corpo, as those are the most interesting roles for such a setting in my eyes or from my preferences.
With you being likely unable to "join" any factions in a remotely formal way, and surely not NCPD nor the big corpo factions, but being able to pick a corpo background, I think I'll roll with that unless the game actually gives me an option to establish good ties with NCPD, or at least certain units of NCPD (coughcoughMAXTACcoughcough). Even if I was able to portray a formal or loose cop due to opportunities provided in the game, a later DLC or a mod, I think I'd like to keep it "humble" with my character concept.
As the main goal and dev statements itself proclaim, I think the base game will be less about super heroes or super hero protagonists. You likely won't be super special V, just someone trying to look after themselves or make a (little?) name for themselves. In that sense, for example as cop, I would've rather aimed at an approach of "You are just one out of millions in this city and try to get by", opposed to, I dunno, trying to be Judge Dredd on steroids.
That is the most fun for me in such stories, being more like an average Joe who gets either by and / or raises up the social ladder a bit or a lot. I also found that in online RP settings (DayZ, ARMA, whatever) rising to the top through gameplay and interactions was way more rewarding and felt more "earned" plus organic than just trying to portray special roles from the get go.
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A bit more concrete:
As I like to add a bit of background or "fill it" for simple immersion's sake, I think my main character will definitely have a corporate background from another place would've done some things already so it fits into the main narrative, too, perhaps spending limited time as "beat cop" in that other city before going the corpo route. They eventually felt it was a dead end and heard that Night City allows a big jump ahead, with more risk involved, so it was an opportunistic move to move on to NC with barely any or no ties opposed to the eventual dead end elsewhere. No dramatic story where they had to flee to Night City due to big drama, just an opportunistic move, a gamble, with a possible clean slate.
