Well... the easiest rule of thumb I've come across to remove hand-shakes is the following:
Shutter speed = 1/(focal length * F) where F = factor of 1.5 to 2
Most places say 1.5 is enough, but to be paranoid you can use 2.
IE shooting with an 18-55mm, 1/100 should be safe for normal handshakes. a 75-300, use 1/600 if you're zooming all the way. Don't forget that EF-S has a *1.6 factor, so if you really really want to be picky, use 1/150 for 55mm shooting.
I personally usually shoot with Shutter priority and toggle 1/200 as my walkaround outdoors. I bump my ISO up to max 400 if needed and let the camera determine aperture. For beginners, just use this method, slowly experiment with the other settings at your leisure.