The first book club I organised focussed on "Introduction to Analytic Number Theory" by Apostol (1976). While the book excelled in rigour, some members, especially those without a strong mathematics background, found the constant alternation between theorems and proofs a bit too dry. Personally, I thoroughly enjoyed it. See <https://susam.net/journey-to-prime-number-theorem.html> for a related post.
For the current book club, I've chosen something more lightweight with a more relaxed writing style. Although I'm slightly concerned about the level of rigour in this new book, I'll be able to assess it better as we make more progress through the book.
Rudin is also on my mind. But maybe that's for a future series of book club meetings!