Mirror: I use the mirror in my front hall and my iPhone. The lighting is poor (if I open the door behind me to let in natural light, it tends to throw me into shadow) but it's quick and easy. I try to stand a bit further back (the closer you are the more distortions/foreshortening you will get) and zoom in slightly. On an iPhone you can double tap a spot to focus/expose there, which helps with the lighting issues. I crop after the fact. I usually hold the phone over my face - hey you all know what it looks like already and that way the outfit is not obscured.
Regular camera: I use a small point and shoot and no tripod. I take them in the bedroom as I get decent light there at least on sunny days (natural light, no big sunbeams or shadows in the morning). I set the camera on the air conditioner in the bedroom window (around waist level) and stand across the room. This is pretty far (maybe 12 feet?) but again the further you are the less distortions. You compromise resolution, but on the high quality setting my photo resolution generally still looks ok after cropping. I use the 10 second, 3 shot timer setting on my camera and check the photos after each round to see if anything needs adjusting. It varies but I can get a decent one in 1-3 tries usually. The background is relatively plain and light colored, which is best for color/light balance. I never use the flash as I hate what it does to colors.
I crop and adjust exposure and color balance using iPhoto or even just the iPhone photo app.
And as others have said, you need to experiment with some test shots around the house to see where you get decent light etc.