I think the most important things are the required features listed in the first post. I do would like to add two:
- Be loggable on a wilfy server (the actual chat being hosted elsewhere). Like we have with irclogs. (Probably this is possible with most solutions anyways)
- Joinable with a little threshold as possible (no account, web based etc.)
IRC is fine with me.
I have use zulip too for some uni stuff. Works rather well!! Especially like the way how one can use TeX code there. Don't know about the logability and the need for accounts (but one can figure out).
A Matrix with some IRC bridge or the like could be an option too.
Have no experience with XMPP apart from the MP lobby.