The font you use in Code view has no bearing whatever on what shows in a
browser.
Use Code view to change the fonts, either by applying CSS to tags or by
amending <font> tags.
Example (using CSS):
In <head> section of page add
<style type="text/css">
body,td,th,p {font-size:80%;font-family:trebuchet, arial, helvetica,
sans-serif;}
h1,h2,h3,h4,h5,h6 {font-size:100%;font-family:trebuchet, arial, helvetica,
sans-serif;}
</style>
and most of the page will be styled at approx 10pt text using Trebuchet.
Trebuchet is fine as a web font, provided it is used as part of a font
family that provides alternatives for PCs where Trebuchet is not
installed - if it is not installed, the next font in the family list will
be used. If a family is not specified, the browser's default font will be
shown (usually Times or Times New Roman).