simple smtp functionality for CentOS 7, how do I set it up?

In a CentOS 7 server, I need extremely simple email functionality. How can I most simply configure my CentOS 7 server to provide the very simple functionality described as follows?

Here is the use case: Two email accounts for the entire server, both of which only handle automated emails managed by a web applications. One of the email accounts is send-only. The other email address will send and receive emails that contain attachments. The received emails need to be accessible programmatically, so that my web application can see each email and extract its attachments.

Here is what I have so far: I can send email with echo "<b>HTML Message goes here</b>" | mail -s "$(echo -e "This is the subject\nContent-Type: text/html")" another@anotherdomain.com. I can confirm that this email has been received by the remote recipient. But when the remote recipient (me on another server) replies to the email, I cannot seem to find the reply on the CentOS 7 server.

I do have postfix and dovecot installed on the server. I would like to just keep it very simple while giving my app direct access to a mail api. I do not need a fully featured mail server. I do not need users to be able to login and check email. All I need are two email addresses that handle automated messages. How can I set this up?

I have read many tutorials and much documentation on this, but all of it seems focused on full featured mail servers that greatly exceed my simple needs.

The answer to this question is a set of explicit, step-by-step instructions. A reproduceable, cook-book explanation for how to accomplish this simple set of requirements. If you have something general to state, please make it a comment and not an answer.

EDIT:

My MX and A records at my domain registrar are:

@     MX     10  mydomain.com
@     A      my.ip.addr
*     A      my.ip.addr
www   CNAME  mydomain.com