JoeP,
If you know you're background check will be clean, it saves time to take the class first, and include the certificate with your app. If not, then apply first. The five references have to be from your county, and not relatives. The longer they've known you the better it looks. All those costs are up front, however you can take your own passport style photo and have it printed at the drug store. Save $10. I would call the Dover Post.
For the class I used Dave Johnson in Bear. Was $150 a number of years ago.