Googling "wordpress twitter plugin" returned 99,700,000 hits.
It's going to take a little research to pick one, but 99,700,000 hits suggests it's possible.
As for what to post, I could set up a special forum that's automatically posted to twitter, and you could cross-post to it just the posts you want to appear in twitter.
That was a really brilliant brainstorm you got there, Jody. I can see you get the ramifications of twitter posts leading people back to the site. Could be momentous. Ride that tiger, kiddo!