Table of contents with roman, arabic, and no page numbers

Here's a possible solution using the tocloft package and the book document class:

\documentclass{book}
\usepackage{tocbibind}
\usepackage{tocloft}
\usepackage{lipsum}

\AtBeginDocument{%
  \renewcommand\listtablename{Tables}
  \renewcommand\listfigurename{Figures}
  \renewcommand\contentsname{Table of Contents}
}

% Centered title for ToC, LoF, LoT
\renewcommand{\cfttoctitlefont}{\hfill\Huge\bfseries}
\renewcommand{\cftaftertoctitle}{\hfill}
\renewcommand{\cftloftitlefont}{\hfill\Huge\bfseries}
\renewcommand{\cftafterloftitle}{\hfill}
\renewcommand{\cftlottitlefont}{\hfill\Huge\bfseries}
\renewcommand{\cftafterlottitle}{\hfill}

% Leaders for chapter entries
\renewcommand\cftchapdotsep{\cftdotsep}

% Add space to account for new chapter numbering schema
\renewcommand\cftchapnumwidth{3em}
\renewcommand\cftsecindent{3em}

% Redefine representation for chapter (and section) counters
\renewcommand\thechapter{\arabic{chapter}.0}
\renewcommand\thesection{\arabic{chapter}.\arabic{section}}

\begin{document}

\frontmatter
\chapter{Abstract}
\lipsum[1]
\chapter{Acknowledgements}
\lipsum[1]
\clearpage
\tableofcontents
\clearpage
\listoftables
\clearpage
\listoffigures
\clearpage
\mainmatter
\chapter{Introduction}
\section{Background}
\section{Objectives}
\chapter{Review}
\section{Test Section}
\section{AnotherTest Section}

\backmatter
\chapter{CODE}

\chapter*{APPENDIX}
\addtocontents{toc}{\protect\addvspace{10pt}}
\addtocontents{toc}{\textbf{APPENDIX}}

\end{document}

Here' s an example using the book class. \frontmatter causes Roman, \mainmatter arabic page numbering. For the appendix, I switch off page numbering manually with \pagenumbering{gobble} and add an unnmumbered \part.

EDIT: Added changed numbering scheme (plus correction of ToC indents).

\documentclass{book}

\renewcommand{\thechapter}{\arabic{chapter}.0}
\renewcommand{\thesection}{\arabic{chapter}.\arabic{section}}

\usepackage{etoolbox}
\makeatletter
\patchcmd{\l@chapter}{1.5em}{2.3em}{}{}
\patchcmd{\l@section}{{1.5em}{2.3em}}{{2.3em}{2.3em}}{}{}
\makeatother

\begin{document}

\frontmatter

\tableofcontents

\chapter{Acknowledgement}

\mainmatter

\chapter{bla}

\section{blubb}

\chapter{foo}

\cleardoublepage
\appendix
\pagenumbering{gobble}

\part*{Appendix}
\addcontentsline{toc}{part}{Appendix}

\chapter{bar}

\end{document}