Does your webmail support something like SpamAssassin that automatically tests for spam? If it does they typically provide a web page that lets you set a threshold for how spammy a message has to be for it to be automatically moved to a junk folder. I suggest you investigate what anti-spam features your email provider offers.
Gmail has its faults but they're very good at detecting spam. They also let you configure an account to automatically, periodically fetch email from a account with another email provider and put it in the Gmail inbox. That way you can leverage Gmails spam detection, message filtering etc. You can also configure Gmail to support sending email from other email addresses/aliases . If you do that somebody has to go out of their way to view headers that are normally hidden by default to be able to detect that you sent the message using Gmail rather than the domain used in the From: address.
https://support.google.com/mail/answ...DDesktop&hl=en (fetching)
https://support.google.com/mail/answer/22370?hl=en (From: address)