AFAIK, when the camera's not on (i.e. when the LED isn't lit, assuming it hasn't been disabled) it takes no power at all (in fact you can swap out cameras while the Pi is on as long as the camera isn't running at the time). How fast the camera can startup depends on several factors: assuming you want a decent exposure and white balance you need to wait a few frames after startup to give the AGC and AWB algorithms time to calculate appropriate values. If you start recording video or capturing frames immediately after camera startup you tend to get over/under exposed images with weird color balances.
How long do you need to wait? How long is a frame? Depends on the mode you're running the camera in. For example, recently people have been experimenting with 6 second exposures (for night shots), but that requires running at extremely low framerates (1/6fps), so still captures actually wind up taking about 15 seconds because of the frames required for AWB. If you know the white balance gains you want to use in advance you might be able to shave some time off by setting them manually, and likewise for the exposure time the shutter-speed can be set manually.
Basically camera startup itself is extremely quick (try hacking apart
raspistill to stop immediately after it creates the camera component and configures it - it should only take a few tens of milliseconds), but the time you need to wait after that to actually get a decent capture will depend on several things including the conditions you're shooting in (might be a fraction of a second for daylight stuff, or 10+ seconds for long night exposures - incidentally this is why most of the examples in the picamera docs have a 2-second delay after initialization - I've found it's a delay which gives reasonable results in most circumstances - though it's probably overkill for many!)
One other thing to bear in mind if you're running headless is that you can disable the HDMI port (
tvservice -o) to save a few mA - nothing like as much as the camera sucks down - but it's something.