Trying "a couple of different fonts" is not equivalent to changing the text encoding setting.
Text encoding determines how the fonts are displayed. If you have a UTF-8 setting, for example - that will be different font display setting from Western (ISO Latin 1). It doesn't actually change the font used, but changes how that font is displayed.
Does it only happen in Safari, or does it happen with other browsers, such as Chrome, or Firefox?
Do you have the same issue when NOT using a browser?
I doubt that the old Font Fanagler utility would be worth using in El Capitan. The font caches for the system are just not the same now. That being said, you can do a quick restart into safe boot mode. (Restart while holding the Shift key. You can release the shift key when you see the boot progress bar begin the load) The Safe Boot mode rebuilds the system and user font caches, and may remove your issue with how the fonts are displayed. Restart normally after that Safe Boot, then check one of your sample pages.