How to add a path to system $PATH for all users's non-login shell for debian

On Debian and other systems that use PAM (which is most of them nowadays), you can set environment variables (including PATH) in /etc/environment. This will work for any login method that uses the pam_env module (either in the auth section or in the session section); on Debian that should be all of them (at least the ones that provide ways to log in and run commands).

The default path could be set in /etc/profile like Joe said but also in $HOME/.profile. I also have plenty of packages i compiled on my own (with the common procedure ./configure --prefix=/opt/<name>) installed in /opt. To execute the binaries in /opt/<name>/bin without any additional effort I added

OPTDIR=/opt

for i in $OPTDIR/* ; do
    BINDIR=$i/bin
    if [ -d $BINDIR ] ; then
        if [ -z $PATH ] ; then
            PATH=$BINDIR
        else
            PATH=$BINDIR:$PATH
        fi
    fi
done

export PATH

to my $HOME/.profile which in your case would be /etc/profile. Now even if i install packages under /opt in the future i don't have to worry about accessing the related binaries in /opt/.*/bin since the path is automatically added to $PATH.

Because the additional software is not necessary stable i prefer $HOME/.profile over /etc/profile.

---

A small remark: /etc/.profile respectively $HOME/profile is not executed by your default shell but by dash. A lightweight variant of bash which reduces the load during the boot process.