Ask HN: How do I solve this?

I am trying to build an app where I want to give users an email id for ex: abc@xyz.com. I am then building a parser for emails received on that email.

My problem is I am not sure how I can do the following : - give each user a unique email id

Google app emails are expensive and hosting my own mail server is complex. Is there a better way to do this? Any service, tutorials, pointers will be helpful. Thanks