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I can certainly vouch for Gmail. Gmail is a mainstream email service for a good reason, a google account grants you access to so many other services (Google drive, YouTube are probably the primary benefits) that I don't think any other service is comparable to Gmail.
But I have used Google Mail for years and have all my different emails separated and filtered into folders. Also to forward emails I just select the option to forward email. The email I then wanted forwarding gets forwarded.......pretty straight forward if you ask me