I definitely recommend using the self-timer rather than the mirror shot. When I did mirror shots, I always got weird reflections (plus they always revealed that my mirror was not as clean as I thought, LOL), the perspective always seemed a bit distorted, and it was hard to get everything in the photo. I have no tripod, and a simple point-and-shoot camera.
You can experiment with locations as well as lighting conditions (never use the flash if you can help it though! take photos during the day!). Also, try taking photos with the camera at different heights (you can put it on a chair, or table, or shelf, table with a stack of books, etc if you don't have a tripod) to see what angle you like best. I take my photos with the camera around waist level, about 6 feet away, using the setting that takes 3 photos in a row after a 10 second delay. I always crop my photos to get rid of a lot of the other stuff behind me in the frame; I just use the built-in crop function in iphoto for this.