What should I prepare for customs when entering Thailand with a DTV visa from Discover Thai Nature?

You should be fine, have a printout of your DTV to show. Useful to have your DTV docs stored on your phone incase of being asked.

You're confusing terms. Many Americans incorrectly call Immigration/Passport Control "customs." Customs are the people who may randomly check your luggage upon entry for prohibited items or items subject to duty. They have nothing to do with your entry into a country. Even in the USA, customs are the people who wave you through or direct you to an inspection station when you present your blue customs form about what you are bringing into the country.

As for your question, some DTV holders have reported being scrutinised and heavily questioned about the activity that qualified them for the DTV, and asked to show that any of the qualifying factors in your application are still met.