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.