How to make binary search trees in an easy and straight forward way?

This is a solution using tikz, as an example consider the following tree

To create this code I used

\documentclass[border = 5pt, tikz]{standalone}

\begin{document}
\begin{tikzpicture}[
  every node/.style = {minimum width = 2em, draw, circle},
  ]
  \node {51}
  child {node {12}}
  child {node {87}};
\end{tikzpicture}
\end{document}

In this representation, it is very clear that both 12 and 87 are children of 57. If you want to grow the tree, just keep adding children

\documentclass[border = 5pt, tikz]{standalone}


\begin{document}
\begin{tikzpicture}[
  every node/.style = {minimum width = 2em, draw, circle},
  level/.style = {sibling distance = 30mm/#1}
  ]
  \node {51}
  child {node {12} 
        child {node {1}}
        child {node {43}
               child {node {36}}
               child {edge from parent[draw = none]}
              }
        }
  child {node {87}
         child {node {52}
                child {edge from parent[draw = none]}
                child {node {83}}
               }
         child {edge from parent[draw = none]}
        };
\end{tikzpicture}
\end{document}

i would simplify tree layout as follows:

and in drawing use package forest:

\documentclass[margin=3mm]{standalone}
\usepackage[edges]{forest}

\begin{document}
    \begin{forest}
for tree={
    grow=south,
    circle, draw, minimum size=3ex, inner sep=1pt,
    s sep=7mm
        }
[51
    [12
        [1]
        [43
            [36]
        ]
    ]
    [87
        [52
            [83]
        ]
    ]
]
\end{forest}
\end{document}

addedndum: considering caverac comment:

\documentclass[margin=3mm]{standalone}
\usepackage[edges]{forest}

\begin{document}
    \begin{forest}
for tree={
    grow=south,
    circle, draw, minimum size=3ex, inner sep=1pt,
    s sep=3mm
        }
[51
    [12
        [1]
        [43
            [36]
            [,no edge, draw=none]
        ]
    ]
    [87
        [52
            [,no edge, draw=none]
            [83] 
        ]
        [,no edge, draw=none]
    ]
]
\end{forest}
\end{document}

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[%level distance=5mm,
level 1/.style={level distance=10mm,sibling distance=24mm},
level 2/.style={level distance=10mm,sibling distance=16mm},
level 3/.style={level distance=10mm,sibling distance=16mm},
font=\scriptsize,inner sep=2pt,every node/.style={draw,circle,minimum size=3ex}]

\node {51} % root
child {node {12} % first level
        child {node{1}} % 2sd level
        child {node{43} 
            child {node{36}} % 3rd level
            child[missing]
        }
    edge from parent }
child   {node {87} % first level
            child {node {52} % 2sd level
                child[missing] % 3rd level
                child {node{83}}
            }
            child[missing] 
        } ;
\end{tikzpicture}
\end{document}