'Normal' is indeed a wonderful concept. ISO standard contrast is about 0.62 (i.e. an increase of 0.62 log density units per log unit of increased exposure) because this gives a negative that will print an 'average' outdoor scene in the area around Rochester, New York, on a midding grade of paper (grade 2 or 3).
But it tends to be sunnier in Japan, so you need less contrasty negatives: if you develop your Japanese negatives to ISO standard contrast, you will need grades 1 and 2. The Japanese members of the ISO standards committee therefore lobbied for a lower contrast (0.56, as far as I recall).
In other words, negative density range is a product of subject brightness range (SBR) and negative development time (more time = more contrast, less time = less contrast). A longer SBR demands less development time for a given negative density range: a shorter SBR, more development time.
To make life still more interesting, we have the lens flare factor to consider. The image thrown upon the film will always be less contrasty than the SBR. If it were identical, the flare factor would be 1, and an SBR of (say) 256:1 (8 stops) would be reproduced as an image of 256:1 (8 stops). A multicoated lens with few elements, in a new LF camera with well-blacked bellows, can come close to 1 but can never reach it. An old zoom in a well-used SLR may well have a flare factor as high as 4. In other words, the image brightness range would be reduced to 64:1 (6 stops). Obviously the lower-contrast image needs to be developed for longer in order to get a negative of the same density range as the high-contrast image.
A 'normal' paper grade will reproduce a negative density range of about 3-4 stops (log density range 0.9, for Grade 3, to 1.2, for Grade 2) as a full range of tones from pure white to maximum black. If the SBR is (say) 128:1 (7 stops, log brightness range 2.1) and the lens has a flare factor of 2 then the projected image brightness range is 64:1 (6 stops, log range 1.8). For a negative density range of 0.9 you need a contrast of 0.9/1.8 = 0.5 and for a negative density range of 1.2 the contrast needs to be 1.2/1.8 = 0.67. All these numbers are rounded for ease of calculation, but they are in the right ball-park.
If the negative density range is less than 0.9 to 1.2, you need harder paper; if it is more, you need softer. Alternatively, you can increase the density range of the negative with more development ("N+ development", in Zonespeak), or you can decrease it with less ("N- development"). If you have a mixture of SBRs on one roll, you can accommodate them with 'normal' development and different paper grades. "Normal", in this context, simply means "the majority of negatives of the sort of subjects you normally shoot will print on grades 2 and 3".
It is perfectly possible to learn all that you need empirically: "suck it and see". Many first-class photographers do this. There are, therefore, only two reasons to study sensitometry, ISO standards, etc. One is that it interests you, and the other is because it's part of your job (as in my case). Once you have studied it, though, think of the Zone System being a small subset of sensitometry, beset with jargon, overcomplicated in some ways and oversimplified in others.
Cheers,
R.