If what you want is private/secure encrypted email that the provider itself can not even read, I recommend you arcanechat.me

Tuta is pretty good and secure but not as fully featured as other providers. For example, there is no way to bridge your email to the client of your choice last time I checked. Still, their client is pretty good. Guess it depends on your needs.

One option i haven't seen mentioned is Startmail. They also have a searh engine that's okay.

Thunderbird?

Are there any good free alternatives to Gmail or do all the good ones cost money?

I assume so since Gmail makes all its money selling YOU…