Replying to myself because I'm sure someone from Zulip will read this thread: I also wish for a tiered channel system. Instead of muting some, I'd like to promote some to high priority, so my inbox can toggle between the ones I really care about and a general overview.

Thanks for the feedback! I think feature closest to what you're requesting is followed topics (https://zulip.com/help/follow-a-topic), which you can filter to in the inbox. Perhaps we could add an option to auto-follow topics in a specific channel to other ways of auto-following topics.

You can "pin" channels. It puts them at the top of the sidebar as well as the inbox. You can also use a variety of filters in the inbox.