You don't say why you wish to use this phrase... I had (with an engineering context as my default) assumed you were describing a sequence - maybe an open ended one.
In both of the dictionary examples quoted, it would be unusual (but valid) to mention the subsequent parts by number. To expand on how the examples could be used in context:
First of all, let me ask you what the subject of your essay is. Then we can follow on with the details that particularly interest me.
Here, the transition from the opening chapter needs to be marked in some way, but you don't need to do that by counting. If you wanted to count, you might get something like this (with a change in emphasis, and a different phrase):
First, let me ask you what the subject of your essay is. My second question would be to know your native language in case that also helps me.
For the second example, you might have:
German unity depends first of all on the German people. There are many other factors that also play their part, but none which are worth listing, let alone trying to rank in importance.
The first of your examples does imply there will be something that follows the begining part. We may never get there (or even define it), but we know it is available.
The second example (where I would choose to use
mostly) is less demanding of any subsequent parts even being mentioned.
This is the British English usage I'm referring to, US English might have different usage