I'm new to Rails and Heroku, and I'm curious about several things regarding production. Do I need to utilize any worker dynos on a simple rails app that has a little email functionality via Mandrill(no queues have been built on my end), and uses Stripe to charge Users upon signup. Also, is it completely wrong to not use a Unicorn server in production, or would it ever be reasonable for a very simple app to use Thin in production. Thanks, I appreciate any guidance!
Do not use WEBrick in production; it is a web server designed for development. You will have a bad time.
It sounds like Unicorn or Thin would be fine for your use case. Don't use workers until you have long running actions that can be done in the background.
Heroku has a "production check" feature that can help you (a little) and make some recommendations: