I've been working on updating the site to use Drupal 7. You might notice that at present, it's still using Drupal 6. There's a reason for that: it hasn't been exactly a smooth process.
First off, you're going to want to make sure you disable any custom modules and custom themes. They won't work initially. Then set your current theme to Garland.
So far, I've run into two empty tables that block the update process. I'm not sure what created them, but it's safe to just drop them: role_permission and date_format_type. (Update: Drupal 7 created them, and the MySQL script I was running to "reset" the database wasn't clearing everything.)