Here's what I do.

Mail coming in from mailing lists is automatically filtered into a folder, one per mailing list. It never hits my Inbox. I use procmail to do this as email arrives, before my email client sees it, but most mail client software these days will do the filtering as well.

Once that's done, it's just a matter of using a mail reader that handles threading properly and which can hide read messages. I read new articles in each group, un-hiding old articles as needed just for context. I never specifically archive articles in the list folders by moving them to an archive folder. The list folders are archive folders. I may one day go through and "expire" mail older than a certain cutoff, but I haven't felt the need to do that yet.

If a message in a mailing list is needed as a reference for an action I need to undertake, I copy it into my Actions folder and deal with it as if it were not a list mail.

I normally use Gnus as my mail reader. It is especially useful for mailing lists, because it originated as a Usenet news reader, and so is ideal for handling threaded discussions and helping you manage which articles from high-volume lists you choose to read. But most newsreaders with decent threading should do fine, especially if they can hide or show articles based on status. Evolution and Thunderbird are both adequate.