If I have a custom shell script or programs, that I created myself or downloaded from the web, and I want to be able to execute this from the CLI, is there the standard location to put this in Linux/Unix directory structure?
/usr/local/bin exists precisely for this purpose, for system-wide installation. For your own private use,
~/bin is the de facto standard.
If you want to keep each binary in its own subdirectory, you can do that, and add a symlink to a directory already in your
PATH. So, for example
curl -o $HOME/downloads/fnord http://fnord.example.com/script.exe ln -s $HOME/downloads/fnord $HOME/bin/
$HOME/bin is in your
PATH. (There are tools like
stow which do this -- and much more -- behind the scenes for you.)