I'm still new to AE, so I really don't know all that much about it. I'd like to take some camera footage and add effects to make it look degraded. Things like making it skip, add white noise footage, have lines show up, have the footage break in and out, etc. Similar stuff to what they did in the movie Cloverfield when the camera was dropped, damaged, etc.
Anyone have any creative advice on what effects may work best?
You should check creativeCOW and videocopilot.net. There is a number of tutorials dealing with "bad TV", "bad reception" and "TV noise". Digital noise can be simulated with a Mosaic effect set to a blendmode like Hue or Luminance, white flashes with solids set to Add blending mode and animated opacity, stuttering with time-remapping. Depends on what you really want.
And nothing beats the real thing. Grab a cheap camera and shoot your stuff while banging the camera around. Or do the same thing with the lens cap on and use the glitches and splurts on black as overlay on other footage.