All the bleaches use some form of peroxide.  Most aren't too stable, so
if you're using an OTC product the newer the better.
    I do tray bleaching in my office.  I try to get patients to use
something like the Crest White strips first.  If the stain doesn't
respond to the white strips it likely won't do much better with my
trays.  You should have a thorough cleaning at your dentist first--any
stain on the surface of the teeth will interfere with penetration of the
bleach.
    Light-activated bleaching "systems" that are heavily promoted, such as
"Zoom" and "Britesmile" are quick and convenient, but are most likely to
cause significant tooth sensitivity (which usually remits on its own,
though it may take some time).  The other risk is burning of the gums if
a concentrated bleach is used and it gets on the soft tissues.
    The Crest White strips have been around longest.  I believe they make a
"professional strength" formula too--don't know if it requires a
prescription.  But generally they all work the same, and less
concentrated bleaches may just need a few more days to work.
    Don't let your kid push you around (at least she was polite)!

Steve
dad to Lauren (age 12)