You always need to backup your database & files before an upgrade.
How to backup database:
http://codex.wordpress.org/Backing_Up_Your_DatabaseAlso there is a nice plugin that will help you with the database backup:
http://wordpress.org/extend/plugins/wp-dbmanager/How to backup your files: Just use a FTP program (like filezilla) to download them from your server.
On the topic of 2.7. I love it. The admin dashboard has tons of features. Plugins can be installed without having to upload the plugin to your server. Plus there a security benefits to upgrading.
You shouldn't lose any cats or permalinks.