In it's basic form you are looking to choose your shading technique based on what you want your end result to look like. I only draw in pencil and usually that is a mechanical pencil or a basic HB2.
Most of what I will refer to here is the first drawing book I really read and used: Dragons: Learn to draw step by step
There are different types of shading techniques like criss cross, straight lines, circular shading, and dot shading
Other names for those are crosshatching (criss cross), hatching (straight lines), circular strokes (circular shading), stippling (dot shading). You also forgot to mention blending and basic scribbling. I am sure there are some other but I think that covers the basics.
The following picture from the book shows some of those shading techniques, done in pencil, in action.
Click image to enlarge and see finer detail
While these techniques are used with pen and ink they are not exclusive to those tools (Blending not so much). Since pen and ink are more permanent then say pencil some guides recommend that you do you rough drawing in pencil anyway. That would include shading as well.
Using pencil is a simple way to get a soft and subtle appearance.
[W]hat factors does choosing shading technique depend?
Nothing really other than your desired end effect. As you can see in the above picture it is still a dragon regardless of the shading technique used. Personal preference would play a large role in this.
You could use a combination of cross and regular hatching as a means of having different levels of darkness but that is not the sole way of doing it. In the end it does not matter and pick whichever one would compliment the work best or whatever you think would look better.