Perhaps this is neither here nor there, but I find it rather surprising that your faculty would require you to typeset your thesis using the Verdana font. Firstly, Verdana is a sans serif font, and traditionally, body text is typeset in a serif font. Secondly, Verdana is a commercially owned proprietary font, and it seems odd to be that a university would require their students to use any particular commercial product (at least not unless they were supplying it to them for free; though perhaps they are.)
The easiest way to use an arbitrary TrueType font is to typeset using XeLaTeX. XeLaTeX is different from regular LaTeX or pdfLaTeX, though MacTeX 2010 comes with all of them, and like pdfLaTeX, XeLaTeX generates a PDF by default. But it does mean that you need to explicitly tell your editor to use XeLaTeX instead of pdfLaTeX to compile. How this is done would depend on your editor. What are you using?
Anyway, if you do use XeLaTeX you can use the
fontspec package. It is a good idea to read its documentation. The right commands likely would be these:
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\usepackage{fontspec}
\defaultfontfeatures{Mapping=tex-text}
\setmainfont{Verdana}
or perhaps:
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\usepackage{fontspec}
\defaultfontfeatures{Mapping=text-text}
\setsansfont{Verdana}
\renewcommand*{\familydefault}{\sfdefault}
If you need Verdana in math mode too, you'll need to look at the
mathspec package.
You'll need to have Verdana installed as a system font for any of this to work.
A lot of the rest can be left out. Let me say a word or two about some of the things in your document, and how they would need to be changed or omitted.
Leave this line out. You should only use
inputenc package with latex or pdflatex; it is not compatible with xelatex, which expects UTF-8 (unicode) input by default. I'm also fairly sure that the applemac option is for pre-OS X versions of mac, which it's unlikely you're using. Most likely, you are using UTF-8/unicode, though it would depend on your editor, and you might want to check. Anyway, you shouldn't use this package with xelatex anyway.
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\renewcommand{\rmdefault}{cmss} %sansserif fond default
"cmss" stands for "Computer Modern Sans Serif", so this does set your default font to a sans-serif font, but not the sans serif font you wanted! Anyway, see my suggestions above for better ways to handle this.
The txfonts package is for using clones of the Times (New) Roman fonts in your document. Loading this will undo everything else, so don't.
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\sectionfont{\fontsize{14pt}{17.5pt} \bfseries} %set font to headline
\subsectionfont{\fontsize{12pt}{15pt} \bfseries \itshape}
\subsubsectionfont{\fontsize{11pt}{13.75pt} \bfseries}
\paragraphfont{\fontsize{11pt}{13.75pt}}
These are options for sectsty; they probably will work OK like this, so you can leave them.
This package is not needed in XeLaTeX; for that matter it's not needed in the 2010 version of pdfLaTeX either.
