Maybe I misread the question, but if you want to vary the type of the arrow you may want to use
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\begin{document}
% based on https://tex.stackexchange.com/a/39282/121799
\tikzset{->-/.style n args={2}{decoration={
markings,
mark=at position #1 with {\arrow{#2}}},postaction={decorate}}}
\begin{tikzpicture}[bullet/.style={circle,inner sep=1.5pt,fill}]
\path (0,5) node[bullet,label=above:$A$](A){}
(0,0) node[bullet,label=below:$B$](B) {}
(5,0) node[bullet,label=below:$C$](C) {};
\foreach \X/\Arrow [remember=\X as \LastX (initially C)]in
{A/latex,B/stealth,C/>}
{\draw[line width=1pt,->-={0.5}{\Arrow}] (\LastX) -- (\X);}
\end{tikzpicture}
\end{document}

As for your comment: this draws three triangles. Is that what you are looking for?
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\begin{document}
% based on https://tex.stackexchange.com/a/39282/121799
\tikzset{->-/.style n args={2}{decoration={
markings,
mark=at position #1 with {\arrow[line width=1pt]{#2}}},postaction={decorate}}}
\begin{tikzpicture}[bullet/.style={circle,inner sep=1.5pt,fill}]
\begin{scope}
\path (0,5) node[bullet,label=above:$A$](A){}
(0,0) node[bullet,label=below:$B$](B) {}
(5,0) node[bullet,label=below:$C$](C) {};
\foreach \X [remember=\X as \LastX (initially C)] in {A,B,C}
{\draw[line width=1pt,->-={0.5}{latex}] (\LastX) -- (\X);}
\end{scope}
\begin{scope}[xshift=6cm]
\path (0,5) node[bullet,label=above:$A$](A'){}
(0,0) node[bullet,label=below:$B$](B') {}
(5,0) node[bullet,label=below:$C$](C') {};
\foreach \X [remember=\X as \LastX (initially C')]in {A',B',C'}
{\draw[line width=1pt,->-={0.5}{stealth}] (\LastX) -- (\X);}
\end{scope}
\begin{scope}[yshift=-6.6cm]
\path (0,5) node[bullet,label=above:$A$](A''){}
(0,0) node[bullet,label=below:$B$](B'') {}
(5,0) node[bullet,label=below:$C$](C'') {};
\foreach \X [remember=\X as \LastX (initially C'')]in {A'',B'',C''}
{\draw[line width=1pt,->-={0.5}{>}] (\LastX) -- (\X);}
\end{scope}
\end{tikzpicture}
\end{document}
