Web-mail is a convenient way to access email if you are not using your own computer.
If you use your own device or computer, accessing your email with real email software is faster, more convenient to manage, and easier to keep secure.
Increasingly email providers use the web experience to scan your emails and show adverts based on the content.
If they do not have a warrant to scan your emails, they should not be looking at them.
Use web-mail only as a backup, not your first choice.