I'll take your question point by point.

> What secure and good options are there for hosting own private mail
> server?

Off-topic: product recommendation.

> is it really worth it to have a separate VPS just for running postfix?

No one can answer this except for you. None of us know your requirements nor how much anything is worth to you.

> Would it be fast and effective? How would it work against spam
> filters?

How long is a piece of string? Honestly, how good are you at administrating an email system? If you're having to ask these questions, it's probably not something you're skilled at.

> Is there a better way to do that from within my google cloud solution?

Off topic: opinion-based.

> Is it a better idea to keep the google cloud website/service separate
> from the e-mail server for security reasons?

Off topic: opinion-based.

> What is common practice in the field?

Too broad.

> Would you advice against or for using SendGrid, Mailgun or Mailjet for
> my daily email?

Off-topic: both opinion-based and product recommendation.

> Would using AWS resolve all of my problems and be better fit for my
> use?

Off-topic: too broad.