Member-only sidebar

OK, so I’ve been looking for a way to do this to no avail. Maybe there’s an answer or plugin out there…

I’d like to go a little further than the template tags for login and register. What I’d like to do is once a member logs in, there’s a spot on the sidebar that appears (it wasn’t there before) having a brief welcome message with the person’s name, a link or two, and a logout option.

And, IF POSSIBLE, I’d also like to be able to put codes into this member-only sidebar, so I can embed a random gallery image into it, too.

Is there a way to do this?