Debian packages the firefox-esr release which works quite well most of the time, but I find often the newest browser is often required for some functionality. I've put together a little script that basically sets this up with a local firefox install in ~/.opt
You can copy/paste this into a terminal and it will download the latest firefox, extract it to ~/.opt/firefox and setup a desktop file so that it will appear in the desktop menu
mkdir -p ~/.opt
cd ~/.opt
FFCHANNEL=latest
LIBDIRSUFFIX="64"
VER=${VER:-$(wget --spider -S --max-redirect 0 "https://download.mozilla.org/?product=firefox-${FFCHANNEL}&os=linux${LIBDIRSUFFIX}&lang=${FFLANG}" 2>&1 | sed -n '/Location: /{s|.*/firefox-\(.*\)\.tar.*|\1|p;q;}')}
echo $VER
wget https://ftp.mozilla.org/pub/firefox/releases/${VER}/linux-x86_64/en-US/firefox-${VER}.tar.bz2 -P /tmp
tar jxvf /tmp/firefox-${VER}.tar.bz2
mkdir -p ~/.local/share/applications
BASEDIR=`pwd`
cat <<EOF >> ~/.local/share/applications/firefox-stable.desktop
[Desktop Entry]
Name=Firefox
Comment=Web Browser
Exec=${BASEDIR}/firefox/firefox %u
Terminal=false
Type=Application
Icon=${BASEDIR}/firefox/browser/chrome/icons/default/default128.png
Categories=Network;WebBrowser;
StartupWMClass=Firefox
StartupNotify=true
EOF
sudo ln -sf ${BASEDIR}/firefox/firefox /usr/local/bin/firefox
More information in the debian wiki: https://wiki.debian.org/Firefox