If you could tell us what theme you use, we could be more specific...but here goes...
When you go to Administration > Plugins > Text editors > TinyMCE HTML editor > General settings> Available fonts list, you can add to the available fonts or change the order of fonts listed in the editors drop down list. BUT, what actually gets set as your default is set by your theme.
On the same settings page, there is a custom configuration box. I have found a number of settings I can place in there that will receive a check mark showing it should be ok, but invariably, my theme over rides them.
I typically use the anomaly theme on my development site and to do what you want is very easy set up, as it has a css file specifically for the editor. In the file located at yourmoodle/theme/anomaly/style/editor.css on line 2 is the default font size, and on line 6 is the default font family. Whatever I set there, is what I get any time I open an editor window. Of course, while editing, if you change the font or size, it does start typing with the new settings. HOWEVER, once it is saved, again there are other settings in the theme that can change the look and wipe out those editor settings. The only way I have been able to get text to be different when displayed, is by using the settings in the editor... it gives me wysiwyg.
Whether or not an editor.css file is in a theme is just up to the theme designer. A quick look through shows that some do and some don't have an editor.css file. If yours does not, you would just have to look through your theme and search for the settings you need modify for what you want.
Basically, to get what you want, you will have to go through your theme files
Hope this helps,