[Answered ]-I'm having trouble deciding between using a foreign key, many-to-many field, or choicefield

What you have actually implemented here is a Many To Many relationship between Consoles and Video Games without using Django’s ManyToManyField. It does seem that a many to many relationship is what’s required here.

The Game model corresponds to a ‘through’ model in django speak. But your Game model does not have any additional fields so it can be dropped completely to end up with just two models.

class GameConsole(models.Model):
    name = models.CharField(
        max_length=8,
        default='PC'
    )

    # console_logo = models.ImageField()

    def __str__(self):
        return self.name

    class Meta:
        verbose_name = 'game console'
        verbose_name_plural = 'game consoles'
        db_table = 'console'
        ordering = ['-name']


class VideoGame(models.Model):
    title = models.CharField(
        max_length=128,
        default='???'
    )
    consoles = models.ManyToManyField(Console)
    # game_cover = models.ImageField()
    # company_website = models.URLField()
    # date_published = models.DateField()

    def __str__(self):
        return self.title

    class Meta:
        verbose_name = 'video game'
        verbose_name_plural = 'video games'
        db_table = 'games'
        ordering = ['-title']

Then it’s possible for you to use Admin Inlines to Games from Console change forms and vice verce

If you want to display many-to-many relations using an inline, you can
do so by defining an InlineModelAdmin object for the relationship:

class GameInline(admin.TabularInline):
     model = VideoGame
     exclude = ('consoles',)

class ConsoleInline(admin.TabularInline):
     model = Console

class GameConsoleAdmin(admin.ModelAdmin):
    list_display = ['name']
    inlines = [ GameInline]

class GameAdmin(admin.ModelAdmin):
    list_display = ['game', 'console']
    inlines = [ ConsoleInline, ]    

admin.site.register(GameConsole, GameConsoleAdmin)
admin.site.register(Game, GameAdmin)