Google charges $6 per user per month, AWS charges by number of emails sent/received.

Why not go with FREE (within some limitations)?

If you are buy domain from a domain provider which supports email forward for free such as namecheap. You can have unlimited number of emails with a considerable number of emails per day.

Firstly, you need to config your setting at domain provider panel for it to forward emails (from your custom domain) to your mail box (e.g. gmail)

Next, register sendgrid API and integrate sendgrid to your gmail inbox. This enables you to send from gmail on behalf of your email at the custom domain.

Sendgrid limits you 40,000 mails for 30 days, and 100 mails/day free forever. That is reasonable if you are using email for personal purpose.

Here is how to setup Gmail to send email via sendgrid:

https://transang.me/how-to-send-your-custom-email-from-gmail-via-sendgrid/