I want to secure a non-public website or application.

To secure a non-public website, an internal website or Faceboook application, securing the connection without proof of identity is in most cases sufficient. Therefore you can use a low-priced Domain Validation certificate. Characteristics of DV certificates are: very fast delivery and extensive support by (mobile) browsers and applications, which prevent browser warnings. For a certificate without organisational data only the registrant is checked through domain validation.