I suppose jeremyjh@ meant emailing someone with a Google account kind of defeats the purpose of self hosting as your message is now at Google's hands. Self hosting probably makes more sense if people you're emailing are self hosting too.
Most hosted mail services have no issues getting to mailbox. I've used Gandi, Mailbox, FastMail, and never have any mails flagged as spam.
Deliverability is only an issue when self hosting (particularly for home IPs)
I mean, at least for me it hasn't been a problem. I currently self host mail on a VPS and everything's awesome. YMMV
>never have any mails flagged as spam
You don't know this for certain, no one can unless you monitor both ends.
Then get a legit-looking domain name and hope you don't get algorithmically deranked. It's literally a gamble.