In my d20 modern game (Poltergeist: The Legacy meets Buffy meets the Bureau 13 novels -- I would have used Supernatural and Dresden Files but I hadn't discovered them yet) I just did a standard "mysterious employer" bit. I had each player figure out a way their character had interacted with the supernatural sometime recently, and had them all start play with an inkling of what was going on.
I decided against drawing out the culture shock aspect, mainly because, well, it's fun for a game or two and then it just gets tiresome (to me, anyway). I figure most people would adapt to the general idea of weirdness pretty quickly, even though particularly horrific situations might still freak them out. I mean, we've all seen Buffy and various horror movies, so why wouldn't our characters have seen them too? Although I guess that's kind of anti-CoC, which is supposed to contain a lot of gibbering, I've heard?
Anyway, it was tons of fun to DM (and my players must have enjoyed it -- they signed up for my next campaign, anyway). I ran with the TV-show idea and divided my plot up into a "season" made up of "episodes" (each sessions was an episode). I also used all sorts of TV-show gimmicks, like starting things in the middle of the action, fast breaks, and having all the "downtime" (healing, shopping, etc.) happen in the breaks in between sessions.
Some ideas that occurred to me for your game:
Figure out your factions. Which major groups of supernatural are running around your campaign area, what do they consider their territory, and why? In a modern setting, you're going to have gangs, corporations, Mafia, small business owners, and so on. Who can the PCs go to for information about the supernatural world?
One of the things I've noticed about the Dresden Files (although I haven't seen that many episodes) is that there are lots of groups circling Harry, and all of them have their own agendas and demands and history with him. Makes for a very tense world when you could tick off any group at any time, or find yourself a pawn of someone you hate by virtue of working to protect the innocent.
One of the coolest aspects of being a hero in an oblivious world is that, like a superhero, you can't tell anyone else about it. Give the players NPCs who are non-initiated. Girlfriends who don't understand why they're always unavailable at night or being called away half-way through that dinner date. An ex-wife who has just been promoted to being their boss. A kid who is keeps getting into fights at school because his dad's cover job is dorky (and watch as they resist explaining that daddy is really a superhero). These are regular Joes, just like you or me, and how many people in your life would be at risk if you suddenly started hunting monsters tomorrow?
As far as drawing them in goes, if you really want to use that option, I'd structure that sequence around situations that are supernaturally ambiguous (see early X-Files). A serial killer who *might* be a vampire -- he drains the bodies, fears sunlight, and won't cross running water, say -- but the body is lost during the final confrontation, so it can't be proved either way. A werewolf who turns out to be a guy with a genetic condition. The heroes are trapped in a haunted house, and afterwards, tests show they were all exposed to some sort of hallucinogenic mold (which doesn't mean there weren't ghosts anyway). Things like that.
