I'd hope most decent providers let you use your own domain...
It's easy to think gmail spam filtering is good if you never check the spam folder. It has filtered out some very important mails for me and others so I do my very best to disable it. Create a filter for "is:spam" and "Never send it to Spam" is the best solution I know. But despite this google might remove mails anyway.
Another big advantage is that their spam data aggregation is optional, unlike Gmail's, and solely uses the content of confirmed spam (aka, you permanently deleted it) to refine their data, so no personal data is getting hoovered up with it.
I did actually shut off offering up my spam data to the masses on FastMail, because I realized I had an edge case where the filters defining my spam as spam for everyone could be harmful.
As far as backup, I have a local Microsoft Outlook which I open every so often which pulls down all the email. I wouldn't mind a Google Takeout-esque download feature from FastMail at some point too though.
I haven't looked into backing up gmail.