Nice looking empty set?

Try \varnothing from the amssymb package. It is perfectly round, and the comprehensive LaTeX symbol list states that it is preferred by many to \emptyset.

\documentclass{article}

\usepackage{amssymb}

\let\oldemptyset\emptyset
\let\emptyset\varnothing

\begin{document}
$\oldemptyset$ $\emptyset$
\end{document}

I always just use "\O" in math mode:

$\O$

I find that { } (\{\} in LateX) is perfectly clear to mathematicians, maybe not to computer scientists. I would use the following:

This is obtained with

\usepackage{algorithm}
\usepackage{algpseudocode}
\begin{document}
\begin{algorithm}[H]
    \begin{algorithmic}[1]
    \State $myset \gets \{\}$
        \For{$i = 0\, \textbf{to}\, 4$}
            \State {$myset\gets myset\, ||\, (4 - i)$}\Comment{append $i$-th reversed index}
        \EndFor
    \end{algorithmic}
\end{document}

Using \emptyset would give

This is obtained with

\begin{algorithm}[H]
\begin{algorithmic}[2]    
    \State $myset \gets \emptyset$
        \For{$i = 0\, \textbf{to}\, 4$}
            \State {$myset\gets myset\, ||\, (4 - i)$}\Comment{append $i$-th reversed index}
        \EndFor
    \end{algorithmic}
\end{algorithm}