Yeah, for art galleries usually you'll be looking at shooting with something like a 50mm f/1.4, at f/1.4-f/2, ISO 400-800, shutter speed 1/50 or ideally faster. Most museums that I've been to will allow photography, but no tripod and no flash. Some allow monopods, which can help in stabilizing the camera, but I still won't go less than 1/focal length for shutter speed (unless I am using an image-stabilized lens; but all my image-stabilized lenses are f/4 so I would be looking at 1/6 or 1/8 second, likely at ISO 800 or maybe even 1600: not totally out of line with IS considered, but not ideal either.).
Nature, outdoors. On a sunny day, typically I will use ISO 100 or 200, f/8 to f/11, shutter speed 1/100 to 1/400. There is the old-school "Sunny 16 Rule" which says that on a sunny day, set aperture to f/16 and the shutter speed to the reciprocal of the ISO (so, ISO 100 = 1/100 shutter speed, ISO 200 = 1/200 shutter speed, etc.). f/16 is excessive for most DSLR's -- I would recommend you stick to f/11 max, until you learn more about the limitations of your equipment (diffraction hits high-megapixel crop sensors usually around f/11 or lower) -- so my rule of thumb would be off by a factor of 2 (if using f/11) or a factor of 4 (if using f/8). So, f/8 and ISO 100, you would go with 1/400 speed. f/11 and ISO 200 would be 1/400 as well. I would not have a problem going up to ISO 400 and shooting at faster than 1/1,000, since my cameras have little visible difference between ISO 100, 200, and 400.
Really, outdoors on a sunny day, you will have many options. If you want some narrow DOF then go to ISO 100 or 50 if you've got it, f/1.4 and 1/8000 shutter speed. But for general purposes I keep it in the f/8 to f/11 range. Generally you will hit a sweet spot in most lenses in the f/8 to f/11 range.
Here's sort of my decision tree:
Shutter speed must be "fast enough". 1/100 is generally fast enough for most shots, and I use 1/focal length as a general rule of thumb beyond that (50mm lens, 1/50; 30mm lens, 1/30, etc.) The slower the shutter speed, the more you have to worry about camera and subject movement. But at 1/100 or 1/200, I know I don't have to worry about anything. (Unless shooting sports or other subjects where extremely fast movement is the norm.) I always go for shutter speed first, unless I am shooting a static scene from a tripod (or using a flash -- in which case, use 1/160 unless needing to balance flash with ambient).
Second thing to worry about is aperture. If there's enough light to shoot at f/5.6 to f/8 then I don't worry at all. All of my f/4 zooms are pretty good even from f/4, so I barely think about shooting them at f/4. In general, I don't have a problem shooting wide-open on any of my lenses, but stopping them down by a stop or two will always improve things. However, depth of field is always a concern. Again, usually at f/5.6 to f/8 you don't have to worry about DOF as long as the photo is properly focused. Of course there are times when you *want* a shallow DOF, and in those cases the aperture might take precedence over the shutter speed.
Last thing to worry about is ISO. I see ISO 100, 200, and 400 as roughly equivalent. I don't really care when choosing between them, and will only worry about it when I need to change the aperture or shutter speed beyond the range where I am comfortable. I will be slightly reluctant to bump up to 800, but not very. ISO 1600 and 3200, I try to avoid, but I acknowledge that there are times when they are unavoidable.