Welcome John. ; Much depends on your camera - if you're shooting with a DSLR, then that F8-11 rule is a pretty good one to abide by when in doubt. ; You can use other aperture ranges as needed, but many lenses do tend to respond best within that range. ; Like Roger, I'd agree you don't necessarily NEED to go off of P mode - more important is to understand the relationship between a given aperture and shutter speed, and how that will affect your outcome. ; You can control the aperture and shutter in P mode too - many people don't realize that! ; I use P mode 75% of the time, yet I am consciously overriding the P mode selection using 'program shift' mode to force a different aperture as needed. ; Also, using a spot meter, you can manipulate the camera's shutter and aperture combo just by pointing at varying light or dark areas within a shot (that's how I control the shutter and aperture on my subcompact, which only has a P mode, and no manual modes).
On that point - if you are shooting with a P&S camera or prosumer fixed lens camera with a smaller sensor (anything but a DSLR for the most part), remember that the aperture values don't have the same range as on a DSLR. ; Where a DSLR lens might give you from F3.5 - F22, making F8-11 a nice sweet spot, a P&S camera might only go from F2.8-F8...making the sweet spot usually something in the middle, like F4.5-5.6.
Hope that helps!