Question marks instead of text

I’m building a site in Greek, I’ve set the encoding to UTF-8 in my settings. Still, visiting the site gives me only question marks instead of the Greek text there is suppose to be. If I change the coding from the browser to Greek ISO 8859 7 it prints out correctly.

Why doesn’t the browser realize it automatically? I have tried to change the WordPress coding setting to ISO 8859 7, no help.

For accessibility, what would be the best way so the browser in use would print the page correctly for everyone?