For me, it's sort of a toss up, depending upon the situation, lighting conditions and what I'm trying to achieve.... Aperture Priority, Shutter Priority and, whenever possible, Manual mode.
I usually leave the camera in Aperture Priority mode since depth of field is often my first and biggest concern.
But I keep a close eye on shutter speeds, too, and if needed to stop action, for example, I'll switch to Shutter Priority mode.
I prefer to use Manual whenever I can. That locks everything in solidly and prevents the exposures from varying wildly due to subject tonalities, strong specular highlights, backlit situations, etc.
I'd note that by "Manual" I don't mean Manual with Auto ISO. I mean strictly Manual.
Manual with Auto ISO is simply a fourth form of auto exposure (Aperture Priority, Shutter Priority and Program). Manual with Auto ISO has it's uses.
I cannot conceive of any good reason for combining Auto ISO with any of the other auto exposure modes... that would make for a double set of variables that's likely to make for less predictable results.
I occasionally use Program, too. No, it's not an "amateur mode". Mostly I just use it when shooting in one situation, then called upon to take a quick shot or two in a very different lighting condition, then return to the work I was doing. In those cases or perhaps when I don't have time to think about my settings and just need to get a shot really fast, I'll occasionally switch to Program. Doing this also allows me to switch back to whatever other mode I was using previously, and still have the settings that I'd set up in that mode.
So I probably use Aperture Priority a little more, but also fully Manual and Shutter Priority almost as much. I use Manual w/Auto ISO and Program the least often.
I never, ever use any of the "Scene modes"... on most cameras those not only choose one or another form of auto exposure, they also often limit other camera setup such as auto focus mode, the type of file being saved, the range of ISOs available, even override things like color saturation and contrast, etc. Scene modes are presets that are probably wrong as often as their right (the same is true of White Balance presets). I want to make my own choices with these things. Scene modes are sort of a carry-over from point-n-shoot cameras, I think. Among the Canon cameras I use, they are more prominent on entry level DSLRs and a lot less so on more pro-oriented models.
Full Auto ("A+" or "green box mode" on my Canon) is another mode I always avoid.... Like Scene modes, it goes way beyond just auto exposure, overriding a lot of things that I want to control myself. For example, in Full Auto or "Super Auto" mode you can't shoot RAW, can't use Exposure Compensation, are forced to use All Points/Auto Selection AF mode (which I almost never use), etc. Like Scene modes, it's probably setting the camera incorrectly as much or more often than it's setting it right!
Incidentally, TTL Flash with Manual camera exposure mode (Canon ETTL, Nikon iTTL, etc.) is a fifth form of auto exposure. With Canon, M + ETTL Flash is "Full Flash", while setting the camera to Av or Tv or P auto exposure modes with ETTL Flash automatically sets it to a "Fill Flash" mode. Both are auto exposure modes.... but in M + ETTL the camera treats the flash as the only light source and controls it's output. In Av, Tv or P + ETTL Flash, the camera sets exposure based on ambient light, as if the flash weren't there, then fires the flash as reduced power fill (usually -1.66 EV). When any flash set to ETTL is attached to the camera, Flash Exposure Compensation (FEC) takes the place of and serves the same purpose as Exposure Compensation, a means of overriding and "tweaking" auto exposure settings. Flash Exposure Lock also works the same with ETTL flash, as AE Lock does with auto exposures without flash. The flashes also can be switched to fully Manual (most studio strobes also are fully Manual), which the user will need to set both camera, lens and flash output.
For me, it's sort of a toss up, depending upon the... (
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