Does it really matter what type of character to start a series with?
Most of the time: Yes.
A lot of longer series have an overarching storyline. I am thinking about Black Dagger for example because the (English) books switch their point of view with every book (as fas as I know; the German ones switch every three books, but I have been told the German ones are basically just the English ones broken into multiple parts).
Basically that series had a group of people doing stuff. They've been doing stuff for quite some time without a lot of action (well, without any difference in the kind of action) happening. And then someone from the outside joined - which is the first character that is used as a main character for a book. This is the point where things start to get into motion. Where new stuff happens. Where new characters start joining over the course of weeks/months/years.
If you want an overarching plot where all the different characters have little stories for themselves you should think about when things start to go from "(relatively) ordinary stuff happens" to "weird/crazy/unusual/dangerous/... stuff happens" and especially which character is somehow tangled up the most in this - for example by thinking about who the first contact with something is. That is your starting character.
Another story with different characters is the "Otherworld" series. There are three sisters. The first book is about "The Witch", the second about "The Cat" and the third about "The Vampire". Then the fourth is from the perspective of the witch again, the fifth from the cat, ...
In this case every character has their own story and their own things to do, but they regularly meet each other. They spend a lot of time together, but the other two don't have so important stuff happening to them personally. The focus is on one of them in each book, even if the overall stuff happening is happening to all of them, possibly at the same time.
Conclusion: The overarching story is what defines which character's turn it should be.
If you want every person to be completely different and independent from each other, except for a few very rare occasion compared to the amount of books you want to write (and that would need to be a lot) then you can go and read the above statement again, in a different light: the events of the time define who's turn it is. You will want to make sure that the reader knows when something happens in comparison to what other books already tell. Therefore you will want to make sure that certain events can be observed from different books and that may give you a timeline you can use to decide which character is influenced the most by an event - which again is your character for the book.
Other than that I would make sure that the first character is very likeable - you want to make sure that people pick up that book, get a feeling for your style and want to read the next one. After a couple of books they will know that each one can be different and they will expect this, allowing you to experiment a bit more - don't take too many risks with the first one.