First off, the editor is not WYSIWYG. It is a rich text editor, but it does not reflect the CSS styling of the theme in the editor window itself.
Each theme is different, it depends on what has been declared in the CSS for each theme. Standard HTML tags for fonts and such are now being replaced by inline CSS as it affords much greater flexibility, so I can give you that code and tell you how to implement it into your pages and posts, but it will have to be done manually for each post and page since the CSS for the theme you have chosen uses a different font. The easiest way to do all this is to wrap the entire post in div tags and then put the inline CSS into the div. Basically you would write your post, and then when happy with the content, switch to the HTML editor and add the following on a blank line above all the content.
<div style="font-family: "Times New Roman"; font-size: 1.5em;>
Then you would scroll down to the very bottom of the post and put this at the very end after all the text.
The font size you can play with to get it like you want it. Doing it this way means you only have to write one little bit of code instead of having to do spans and such. Also, the span tag is typically used only for a word, or a few words rather than for entire paragraphs.
What might be better for you, if you are going to continue with this theme but want to use a different font for everything, would be to use a blog client such as Windows Live Writer or BlogDesk for Windows, or Ecto for Mac.
The other alternative if you have any CSS experience would be to get the CSS upgrade and change the font and font size there so that you did not have to do it on a post by post and page by page basis.
Either that or consider switching to a theme that already uses a serif style font.