<p>I'm interested in hearing people's thoughts about the pros and cons of database mirroring vs. log shipping in this scenario: we need to setup a database backup situation wherein there is exactly one secondary server that need not automatically pick up when the primary fails.  Recovering and starting with the secondary should not have to take too long though.  </p>

Switching to the secondary database does take longer with log shipping, but it's not too bad.  You'll have to manually copy any uncopied backup files, apply the transaction log backups to the secondary database, recover the secondary database, and change its role to primary.  If the old primary databases accessible, you should back up its transaction log before beginning.  Failing over with mirroring is somewhat simpler, and can be done automatically if you are using High Availability mode.  Even when using High Performance mode, it's still a one statement operation.