What I want:

A blog.

I can tag posts, e.g. "A" or "B" or "all," and then you can either 1) click to only view posts tagged "A" or "all" or 2) even more ideally, I can set it so you automatically see posts tagged "A" or "all" when you log in.

LaTeX support--I can type in LaTeX in the editor and it will show the math properly.

No anonymous anything--must sign up and be logged in to view and comment

Not as important, but convenient:

Admin controls, e.g. detailed statistics, see who posts or views what when, control who posts / views, etc.

Hosting:

Ideally, if there's some software I can install on "my" own server, that would be ideal.

But if we can't host it, it'd still be good to find some free (or maybe even paid) service elsewhere that would host the blog if it provided those tools.

Any thoughts? I have no experience with this.

Thanks!