Have you played around with Grafana? It really is quite simple if you have prometheus already working.
For a home lab environment you dont even need to use prometheus-alertmanager. Grafana can handle alerts as well.
Grafana also has hundreds of pre-made dashboards you can import. Node monitoring is quite straightforward.
Assuming you have prometheus good to go, all you need to do is go to Grafana - Datasources, create a new datasource, point to your prometheus instance.
Then you can import the dashboards you want.
Now you can setup your alerts - you can use SMTP, telegram, slack among others for your notifications.
I have a domain with one of the new TLD which I used for my emails.
Most services worked fine with it, but there were a few cases where my email was flagged as fraudulent and I had to call, explain it was legit and provide with another email.
There was one service I registered which explicitly said they oy accept gmail addresses.
Roughly one year ago I acquired a new domain using the .org extension, I am migrating my accounts to this one, and I havent had any problems so far.
So overall my conclusion is that most services are fine with custom emails, a few of them block based on TLD and an even smaller subset will allow only specific providers. Since I am moving alway from big corp, having a widely used TLD that seems to be accepted in most cases is my personal sweet spot.