I shoot in Aperture Priority mode all the time. For ISO settings I keep it on automatic almost all of the time. Generally the only time I go manual is when I'm doing low-light work, and even then I'm adjusting it based on the shutter speed, trying to get the ISO to be as low as possible while not getting the shutter longer than I know I can hand-hold. I've also used it to nudge shutter speeds up; theoretically using shutter priority mode or even full manual could have the same effect, but again I'm boosting the shutter speed to an acceptable level without exceeding an ISO value that I'd find unpleasant to process.
Admittedly, part of the reason I work this way is because it's easy to do on my Olympus. The camera is constantly changing the values based on the scene before me in real-time, so if I see numbers that I dislike I can quickly take over and force the ISO to be something else with one of the control wheels. With my Fujifilm it only shows me what the ISO setting is (automatic and what the maximum allowed ISO is); I have to half-press the shutter if I want to see what ISO value the camera has chosen. It's also a bit more annoying to change the ISO values with the Fujifilm than with the Olympus - the Fujifilm has a dedicated dial for ISO that I don't find easy to adjust without looking away from the viewfinder. While the dial does have a setting to allow control of the ISO via a control wheel, the main control dial is either dictating the ISO in some form, or it's in full automatic. Comparison with the way Olympus does it shows why that's inferior: with the Olympus, it's in automatic until I adjust the control wheel I assigned it to... but I can "wheel" back to automatic as one of the settings. It makes a lot more seamless to quickly shift into and out of automatic.
The Fujifilm does have multiple auto ISO presets that I can set and activate quite easily, and I make use of those instead of fiddling with the ISO directly. Olympus lacks that feature (at least, in my model), but that's fine: I prefer the way Olympus does things anyway.