Owning a domain for yourself and having a provider send/receive email on your behalf is a common choice, and it has its own benefits such as being able to migrate to other providers easily. As long as you renew your domain properly, it should be fine. Though do note that only you would use that domain, so anyone would know it was you who sent that email.

Owning a domain for yourself AND handling email sending/receiving can be challenging because there’s a chance your email gets filtered as spam, and the receiver doesn’t get what you sent. It’s also possible that your server goes down, and the email sent to you doesn’t arrive properly, though the email server usually try to send again a number of times before giving up.

If you are confident about setting a server, I can personally recommend Mailcow. As long as you set up SPF, DKIM, DMARC, it should pass most spam filter including Gmail. If you don’t want to deal with the potential headache, getting a provider to send/receive emails for you is a good choice too.