I dont understand the downvotes on some of these anti-signal arguments. There are a number of very valid arguments against Signal if privacy is your chief concern: they have centralised servers, they've been extremely lax with adding their production updates to their publicly available source code on github, they receive funding from RFA.
Seen a lot of different opinion in this, but personnaly I would recommended this.
SimpleX, for the most privacy (but not really appropriate here)
Wouldn't use any of threema wire and else, as it's not the best.
A good option in the case of this project is a matrix server, if the group is public it's the best thing. Try to host it somewhere else than matrix.org.
Will have no real hiding but surely anonymously if done correctly
signal seems really good right now, with open source clients, but they already show that they'd like to keep the ecosystem locked down by not allowing 3rd party clients. at some point they will need a way to pay for their datacenters, and even if they claim the foundation or whatever is doing well, i can see the pestering for donations getting much worse in the future.
that said, threema is far from optimal too, im still waiting for matrix servers to become solid options. last time i wanted to set up synapse, the only captcha they supported was fucking Google captcha :|