Is There A Way To Keep Very Noisy Mailing Lists Out Of Your Gmail Inbox And Still Participate In Them?

I am trying to keep a noisy mailing list out of my Gmail inbox (and I don't want to switch to https://Inbox.google.com just yet). It's not a noisy list per-se; there's a lot of signal (good information) but I'd prefer to keep it out of my inbox, except for the few posts that I participate in. I don't see a way to do this, which has convinced me to use Google's Inbox app.

Google Inbox combines many similar emails into bundles, either from a mailing list but also by the type of message, for example, groupon deals) into a single item in your inbox. It's basically a way of creating email filter rules but at the same time, alert you when there's a new message (new mailing list post, new groupon) without crowding your Inbox with each new message.

By the way, does anyone else have a huge Gmail inbox? Mine has 300,000 unread messages, going all the way back to 2005 when I first created it. Thank you to the poster from alt.games.mame who sent me that precious invited, back when Gmail was invitation only! It just got out of control and unmanageable. I do skim over all of the subject lines and read emails directly but I don't open reach one.