LaTeX has several ways of setting leading without changing anything else, including:

• \fontsize{default font size}{value of leading}\selectfont

• \linespread{ratio of leading to original}

• \leading{value of leading} % requires the leading package

Some go in the preamble, and some go in the body of the text.

I would like to use the first way above (\fontsize) exclusively, because I can set font size as well. Does this have any advantages or disadvantages compared to the other ways?

You don't want to use the first way, unless indirectly, by redefining the meaning of all font size changing commands: \normalsize, \large, \Large, ..., \small, \footnotesize, ...
The reason is that any command that internally uses \normalsize (or another command of the series above) would spoil your hand crafted leading. What are these commands? To begin with, there is \begin{document}; also \caption, \begin{figure}, \begin{table}, \marginpar call \normalsize; not to forget that it is issued during the output routine, for setting headers and footers.
Where do the definitions you need to change reside? In .clo files; for the book class they are in bk10.clo, bk11.clo and bk12.clo, corresponding to the initial option given to \documentclass. For other classes there are different files (you can see which one is loaded by examining the log file).
The method with \linespread and \leading are equivalent, the second is perhaps easier to understand.
Using explicit \fontsize commands in the document is not recommendable, in my opinion.