How to install MSYS so that it recognizes non-MSYS binaries?

How do I cleanly "integrate" MSYS with the rest of my system?

I use Cygwin (which is similar to msys in the way it works) and selectively add parts of my Windows PATH to my bash PATH as follows:

I have a file (.path_elements) containing the directories I want in my bash path:

/home/DavidPostill/bin:
/usr/local/bin:
/usr/bin:
/c/Windows/system32:
/c/Windows

Note: if you add lines to your .path_elements file they must be terminated by : (except for the last line).

I modified my .bash.profile file as follows:

#DCP 20151019 comment out the original code for setting PATH
# Set PATH so it includes user's private bin if it exists
# if [ -d "${HOME}/bin" ] ; then
#   PATH="${HOME}/bin:${PATH}"
# fi

#DCP 20151019
# Build up the path using the directories in ~/.path_elements
unset PATH
while read line; do 
  PATH="${PATH}$line"; 
done < ~/.path_elements

...

#DCP 20151019
# Add current directory to path
export PATH=".:${PATH}"

Now in my bash shell:

$ echo $PATH
.:/home/DavidPostill/bin:/usr/local/bin:/usr/bin:/c/Windows/system32:/c/Windows
$

You should be able to do something very similar in msys.