There are Serif fonts like Times New Roman, Slab Serif fonts like Bree Serif, Sans Serif fonts like Calibri, Arial, etc.
Times New Roman is well known but here is a sample of Bree Serif:
My question is where to use these three different kinds of fonts? Serif, Slab Serif, Sans Serif... Where are they best suitable for? Headings, books, book covers, newspapers, magazines, brochures...
There are no rules.
There is no "best used for X" regarding any typeface.
This is all what a designer's aesthetic eye has to determine for each piece designed and the goal of that particular piece. i.e for a lot of copy in print, a serif may work best... but if the goal is to promote a more "informational" atmosphere a serif typeface will be contrary to that.
Is all up to you what kind of font you use. Beside the display fonts (that are designed to be used on headings) you can chose whatever font you need to create the desired mood for you page (even Comic Sans).
For web design you should also take into consideration the performance of the page before you chose the mood of the page. If you load too many fonts (with many weights) the page will load too slow so you will have to optimize this by doing more with less. For example you could even use the fonts that are already available on the device of the user by using OS fonts or popular fonts like this:
p{font-family:-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Open Sans", "Helvetica Neue", sans-serif}
