A password manager because if anything goes wrong, you'll be completely screwed.

What you SHOULD absolutely self host though is a password manager, so you can be in control of your most sensitive data.

Regarding email, I think everyone should absolutely self host it, but it's less and less viable in this google/Microsoft duopoly world. But ideally everyone would self host it. The reason why people advise against it really comes down to lack of real competition, and the two tech giants dictating how we violate every RFC possible.