>Thank you very much for your message.
>First, Exchange back end is out of the question. I don't have the skill and the resource for it.

The main issue is you would need a different e-mail address, such as one on outlook.com. Otherwise, the difficulty level in getting set up is similar to Gmail.

>I will need to figure out what my iPhone and iPad use for connecting to the Gmail server. It is not clear if it is POP3 or IMAP.

I believe iOS defaults to trying IMAP and using it if available. But if you set it up a long time ago, or set it up manually it might be POP3. Account type should be visible in the mail account settings.

>In the Outlook, I will need to move the message(s) from the .ost file to a .pst file (where I have folders for different purpose). This way, I will not rely on the .ost file. And having email messages in a .pst file will provide a good storage.
>Does the above make sense?

Don't get fixated on the ephemeral .ost cache file. You don't move items from there to a .pst, you're moving items from the Gmail server to a local .pst file. You probably don't want to do that - if an item is removed from the Gmail server, it will disappear from other devices once they sync.

If instead you copy items from Gmail to your local .pst, they will still remain at Gmail and be visible on your other devices.