Well I think I got the idea...
Using DR and BTS2 (possibly N&SS and SF as well), I'm going to have the players generate characters that are recruited to be part of a government agency that is specifically tasked with keeping the things that go bump in the night from becoming known to the general populace (ie: the PCs are the ones who enforce the conspiracy).
After they get a few assignments done (a build up to the main event), they start to notice a pattern to events and then, just when they get the puzzle pieced together, the Wave hits full force.
I think this will not only give the players a feeling that they could have stopped it but also give them a greater sense of loss when the whole world goes to hell.
As for types of missions I'm going to go for a combination of X-files and Hellboy, some they have to use subtlety (this will be a stretch for my usual group) others they get to employ the methods they seem to prefer, kick in the door and shoot till the questions are no longer relevant.
Questions, comments and suggestions will be welcomed at this stage.
