....

b) avoid the graphical login
edit /etc/init.d/slim (i have lightdm so I show you what I did)
do with your editor
vi  /etc/init.d/lightdm
shift the "2" from line Default-Start to the line Default-Stop
result must look like this

#! /bin/sh
### BEGIN INIT INFO
# Provides:          lightdm
# Should-Start:      console-screen kbd acpid dbus hal consolekit
# Required-Start:    $local_fs $remote_fs x11-common
# Required-Stop:     $local_fs $remote_fs
# Default-Start:     3 4 5
# Default-Stop:      0 1 2 6
# Short-Description: Light Display Manager
# Description:       Debian init script for the Light Display Manager
### END INIT INFO

now do

update-rc.d lightdm remove
update-rc.d lightdm defaults

should apply similarly to slim
worked on my desktops

do

init 3 

to start your graphical login

BR

This did indeed work for slim also.

I also found the reason I was not getting a console login prompt was because I had added a rc.local entry and it was hanging, when I removed the entry the console login appeared as expected.

Thanks to everyone for their help.

If you upgrade LMDE2 to LMDE3 and apt-mark hold sysvinit-core, you end up with dual boot where sysv manages to go graphical but systemd doesn't. Can't figure out how to keep this config through to buster/beowulf, sadly.,

...
# The default runlevel.
id:2:initdefault:
....
# Format:
#  <id>:<runlevels>:<action>:<process>
#
# Note that on most Debian systems tty7 is used by the X Window System,
# so if you want to add more getty's go ahead but skip tty7 if you run X.
#
1:2345:respawn:/sbin/getty 38400 tty1
2:23:respawn:/sbin/getty 38400 tty2
3:23:respawn:/sbin/getty 38400 tty3
4:23:respawn:/sbin/getty 38400 tty4
5:23:respawn:/sbin/getty 38400 tty5
6:23:respawn:/sbin/getty 38400 tty6

the 6 lines shall not be commented out.

in Runlevels 4 5 you have only one text console !

b) avoid the graphical login
edit /etc/init.d/slim (i have lightdm so I show you what I did)
do with your editor
vi  /etc/init.d/lightdm
shift the "2" from line Default-Start to the line Default-Stop
result must look like this

#! /bin/sh
### BEGIN INIT INFO
# Provides:          lightdm
# Should-Start:      console-screen kbd acpid dbus hal consolekit
# Required-Start:    $local_fs $remote_fs x11-common
# Required-Stop:     $local_fs $remote_fs
# Default-Start:     3 4 5
# Default-Stop:      0 1 2 6
# Short-Description: Light Display Manager
# Description:       Debian init script for the Light Display Manager
### END INIT INFO

now do

update-rc.d lightdm remove
update-rc.d lightdm defaults

should apply similarly to slim
worked on my desktops

do

init 3 

to start your graphical login

BR

apt install lightdm
change line in /etc/default/grub to:
GRUB_CMDLINE_LINUX="text"
run update-grub
apt remove slim

On reboot, I see a [warn] message from lightdm saying it found 'text' in kernel command line and would not start.

Same result as before when I disabled slim, there is no login prompt so something is missing which gives the console login prompt.

You mean on restartup or startup? For restartup, uninstalling the graphical greeter is perfectly acceptable. To change at startup you'd have to login as single user and uninstall or disable the greeter

By startup I mean when booting up. 
I found when I disabled slim, it did not go into graphics mode but it also didn't give me a login prompt.  It was still possible to ssh into the machine though.

It isn't possible to uninstall slim, when I try that, apt wants to remove most of the OS (or at least everything to do with graphics).

Just need to figure out how to disable it on startup (I don't want to completely uninstall it).

You mean on restartup or startup? For restartup, uninstalling the graphical greeter is perfectly acceptable. To change at startup you'd have to login as single user and uninstall or disable the greeter

A hack, to disable it, is to create a large file that leaves you with enough free disk space to boot but not enough to run the greeter. When you get your login, rm that file, and you can stay right there, or startx.

I will try sysv-rc-conf and see now that goes.

There are many ways to do so. For example, you might install sysv-rc-conf and run that in a terminal so as to "untick" the box for slim at run level 3, and then reboot with grub set to use run level 3.

I haven't tried this myself but I believe it's sufficient to avoid slim at boot up.

Just need to figure out how to disable it on startup (I don't want to completely uninstall it).

I can see the word runlevel 3 scroll by just before it switches to the gui login.

I have a GRUB_CMDLINE_LINUX="text" in /etc/default/grub.

I assume that you ran update-grub to change /boot/grub/grub.cfg?

This should have put a 'text' parameter in the linux /vmlinux.. line of your grub.cfg's menuentry.

This will start you in text mode, not sure if this will then permit you to successfully run startx - it is implemented as a simple trap in the lightdm init script (/etc/init.d/lightdm):

case "$1" in
  start)
        CONFIGURED_DAEMON=$(basename "$(cat $DEFAULT_DISPLAY_MANAGER_FILE 2> /dev/null)")
        if grep -wqs text /proc/cmdline; then
            log_warning_msg "Not starting Light Display Manager (lightdm); found 'text' in kernel commandline."
        elif [ -e "$DEFAULT_DISPLAY_MANAGER_FILE" ] && \
           [ "$HEED_DEFAULT_DISPLAY_MANAGER" = "true" ] && \
           [ "$CONFIGURED_DAEMON" != lightdm ] ; then
                log_action_msg "Not starting Light Display Manager; it is not the default display manager"
        else
                log_daemon_msg "Starting Light Display Manager" "lightdm"
                start-stop-daemon --start --quiet --pidfile /var/run/lightdm.pid --name lightdm --exec $DAEMON -b|| echo -n " already running"
                log_end_msg $?
        fi
  ;;

In my case this is on my mail server and I just run it headless and ssh -X into it from my desktop PC. Graphics mode (Cinnamon desktop) is installed as I used it when configuring the server and it's there if I were to need to work on the server with a keyboard and screen plugged in on my desk.