I also self host but on a VPS. Incoming mail works great. Outgoing mail not so much unless I send it to a trusted third party SMTP server. No outgoing mail fees if low traffic. Might be an option to consider while building up reputation?
I assume that's because I had no reputation, although I did start on a DigitalOcean VPS before I learnt about their terrible ongoing reputation for ignore abuse reports. [1]
[1]: https://discourse.mailinabox.email/t/digital-ocean-ips-being...
Yes, spam will still make it through and you have to train the filters in either case.