If bracketing for HDR, between 1 1/3 and 2 stops if doing 3 exposures, or 2/3 to 1 stop if doing a 5 exposure set. Depending on the situation. I do 3 exposures at 1 1/3 stops and that covers most situations (I believe that's the default on my D90)
If you aren't doing HDR, but want to bracket for safety reasons, probably +/- 2/3 of a stop.
If you are doing HDR or blending multiple images, you want a fixed aperture, so use Aperture priority or Manual. If the aperture varies you'd get images with different DOF and probably weird effects when you try to merge them.
I usually prefocus, then set to MF, metering set to Manual, and use the high setting for 4-5 frames per second and fire them off quickly. I can avoid using a tripod that way. Too much movement and most HDR programs don't do a good job in aligning and ghost removal in my experience. My self timer will take multiple shots, so I often set that to 3 shots, then I can steady the camera and let it take the shots without having to mash down the shutter release 3 times.
If on a tripod I always use the self timer trick to take the 3 exposure set.
I don't really give ISO any more thought than usual, just keep as low as I can for the situation.