This answer became a little complex because there are different factors involved. So it is not a straight answer, but a series of cases.
The answer to "Where to use Rich Black, which type of rich black, or should I use it at all" depends on several factors, like
The size of the black element. You could use rich black on a big element but not use it on a small one.
How this element interacts with another element. For example, you could need a rich black background interacting with a black photography.
Where you are using photographs or gradients or not.
The quality of the press, of the registration.
Type of paper.
(I will be using CMYK in lowercase because it is easier to read the values)
First of all, what is rich black?
Normally in a full-color print, the black used is not a "deep black" but a washed one, a grayish one.
So rich black is adding some more ink to obscure it.
1) Old, pre-digital era values.
(Obsolete. Avoid using these)
One old type of rich black was adding some cyan. Only one additional color because it was easier to align two colors than 3.
Why adding some cyan to the black, and no magenta? Because magenta casts a very dominant color to the mix. Besides a registration problem with cyan and black is less noticeable than magenta.
(In the following 2 examples the offset is exactly the same)
2) A registration problem
Is more evident in small letters, more on serif fonts and even more on white over black. So you have to decide what is the minimum size you can handle.
3) But let us forget a little of the registration problems.
One big reason to use rich black is where you can compare other blacks and see that some are really black and others are not.
If you have a photo with a black rectangle next to it, the color (and the image) need to match in colors usage.
In some cases, you could print with just black (a). In most cases, the color will look dull, but if all the publication is just one black ink you could pass the black twice (k100k100)
The combinations of C+k and C+M+K does not work (b,c) because you can cast a color that is more visible when you have shades. If you need to do this you probably need to edit the curves to reduce the cast. But I prefer just using them, which I call the "profile black" (d) and my images need to be converted to black and white desaturating them, not converting them to grayscale (e).
I never, ever use the "old values" anymore.
4) What is this "profile black"?
It is the resulting CMYK values after converting an r0g0b0 bitmap with a specific CMYK profile. The values I am using, c75m68y67k90 are of the SWOP2 profile. This is different from Gracol, Fogra, etc.
But in general terms, the combination is like 3/4 cyan, some less percentage of magenta and an equal amount of yellow, and not pure black.
The magenta and yellow are a bit less than cyan but you have two inks that become red. And this red+cyan neutralize each other.
You do not have pure black to improve ink adherence.
5) Ok now let us explore how inks interact with the background
Using some examples of how to add a shadow to an object, we can have different ink values.
k100 using a blending mode multyply.
"profile" cmyk black (described above)
Or using the same values as a flat color below + black.
At first sight, they all work, they cast some black on the print.
But analyzing how the cyan plate reacts to the values we see some problems, mainly that this background color starts to disappear. So not all black combinations work when interacting with a background.
6) Lets go back to the registration problems
With this same black combinations, we can have some white lines when we have registration problems, between two colored zones. So we need to choose a correct color combination.
Using a k100 with the multiply blending mode works similar to using an "overprint" option on the black plate. Overprint is not necessary the same as rich black but is very similar.
7) The main issue, registration problems
Besides obvious quality issues, brand, etc. Some big machines have some registration problems because of a small deformation on the center of the sheet.
In general, if you work with a better quality equipment you can use rich black on smaller elements.
P.S. You do not use all colors to 100% because they will sum 400% of TAC. This will create problems like the inks not drying and making smudges and a mess on the next sheet of paper.