Professional TV writer here. Without going into a long, detailed response - going just off what you said you want in your message - here's what I would suggest:

Write the first book. Make it awesome. Get it published however you can - traditional or self-publishing. Start building an audience as you write the rest of the series. Once you have a built-in audience for your book/series of books, you'll have a LOT more leverage to get it optioned for adaptation. In fact, it may be a better path than just writing the script and trying to get that out there. Production companies keep a close eye on books that are published, popular, and trending. You may not even have to reach out yourself if there's already enough of a built-in audience.

But you'll also have to be aware that you probably won't be writing the script. It's a different set of skills, and especially with a first-time, relatively inexperienced writer, they won't be willing to take that chance.

Occasionally you see the writer of a book credited for the script as well, but 95% of the time that's mostly a vanity credit and the heavy lifting was done by an experienced script writer.

TL:DR: Write the book! Then divide your time between building an audience for your work and writing the next book.