I want to start a mailing list. What software/website should I use?

I don’t have an always-on connection, so I suppose I have to go with something like the Yahoo groups or clubs idea.
One nice thing about those is that you get some space to share files. That’s not essential though.

Its going to be a small list, probably by invitation only. Since it is mainly for the purpose of arranging meetings and activities for our group, I would prefer something that is at least nominally secure, in case someone wants to post their phone number, directions to their house or such.

So does anyone have any recomendations?