If you want a custom domain email address, I typically will recommend that you use a reputable email provider like G Suite or Fastmail. However if you’re just starting getting started and you’re not quite ready to pay for email services, then consider setting up an email forward instead. A great email forwarding service like ForwardEmail.net would suit most folks just fine.
Free email forwarding with ForwardEmail.net
With ForwardEmail.net you can setup any domain name to forward email to anywhere you’d like. That means you can have info@my-amazing-awesome.site send to my-super-generic@gmail.com account. It does require extra DNS configurations as explained here. Amazing Forward Email does this with privacy in mind and is completely open sourced.
Limitations with email forwards and not recommended for regular business use.
The biggest thing you can’t do with a forwarded email address is reply from that address. That means anyone sending you an email using info@my-amazing-awesome.site will see your reply come from your my-super-generic@gmail.com.
That’s really what it comes down to. Are you OK with people seeing your personal email address? If so then feel free to use a free email forwarding service rather then paying for email services. However for many business folks, I’d highly recommend actually paying for email services.