I have all my newsletters delivered to address+news@domain.com and filter them into a folder. You could create one folder as a newsletter “inbox” and one as an “archive”.
Instead of tags, you _could_ have rules file messages into separate folders, but I prefer having all the mail in one folder and using tags that can be applied in a boolean AND/OR method, so I can view "all messages tagged both [Important] and [To Do]" for example. I may have some messages that are important but have no action that are only tagged "Important", or messages that are actionable but not important which are only tagged "To Do" ... but, it's important for me to keep on top of those messages that are _both_ "Important" and "To Do" so I don't let them slip.