I run a small Ubuntu VM on Azure. It is like $10/month. I chose Azure because I get a credit with my Visual Studio subscription.

However Microsoft does not allow outbound SMTP port 25 from Azure by default. It is possible to get them to allow it, but I do not know their criteria, as I've never done it.

I try to avoid running my own mail infrastructure. Even now when I need scripts to send mail, for reports and such, I'll use a service like Sendgrid instead of mucking about with Sendmail. It is just too easy to do it wrong and end up in a black hole.