As far as I understand does neither the w5100 or ESP8266 libraries support TLS / SSL. Are there other boards that supports that? The SMTP providers I use require TLS or SSL authentification.
If you have an Arduino that uses a shield, none of them have TLS/SSL capability.
The least expensive way to do what you want is a RPi as a MTA.
Ok. I will then use a tiny router (GLinet) and openwrt. It is probably even cheaper like 20 USD.
What a pity
I have not tried one, but the WiFi shield 101 shield supposedly has TLS capability.
I have a suggestion, if you don't require end to end encryption. You can create a google appengine app, then do a http request to the app, and use the app to send your email, appengine has an email API. I have been using this method to relay all my outgoing web communications, as arduino/ethernet shield don't support SSL. It also gives me a single centralized location(app) to process all my outgoing comms.