Your solutions are quite understood. Therefore I would suggest selecting the one solution that requires fewer steps:
1st solution
(3 steps) Get newsletter - Write email address - Press button
2nd solution
(2 steps) Write email address - Press button
Therefore, I would go for the 2nd solution.
Also, have a look at this article about how to use modals in mobile. It has some interesting thoughts, on where to user modals:
Interruption: Forcing the user to make a decision or complete a task
at an important part of their workflow. Ask yourself, “do I really
want to interrupt the user?”
Feedback or Correction: Confirming
decisions. E.g., “are you sure?” moment.
Deep Dive: Focusing the user
on a single piece of content, be it an image, article, or a video.
http://uxmag.com/articles/modals-on-mobile-how-to-use-them-wisely