Does it make sense to register in directories at the initial promotion of a very young site?
If yes, please advise which catalogs are better (let them be paid / free).
To begin with, you should start with Yandex and Google.
https://webmaster.yandex.ru – link to registration in Yandex https://www.google.com/webmasters/ – link to registration in Google
If your project forces users to stay on the site, this will only play a plus.