Update
For the contact collection we are still using ninja form, which makes us manually adding the emails to the newsletter tool, PhpList, that we are now using.
Simplest process, is to use a simple script so when someone fills his address through wordpress it is actually sent to phplist. Here is an example:
http://timssandbox.owiowi.net/?page_id=317
When the process is approved we can implement it on the official wp