I cannot say I know of anyone that has a dog that hunts squirrels and rabbits and then onto coons and upland game birds, BUt sure some dogs with enough drive and training can do it,
as you already know, the game animals your naming all have different ways of life and this is why some breeds do ONE type better than others, dogs that are runners like beagles and con dogs, tend to be HARD to have self control to hunt birds(upland game,) as they prefer to keep moving, your not going to get them IMO steady to a flush or shot
you will HAVE to be willing to have a dog that will never really be finished on anything, but just TRY hard at all
IF I was to pick a breed of dog that has a rep for being very multi talented it would be a The Deutsch Drahthaar,
they have been known to be very versatile dogs , take well to training and very durable dogs
not so sure about being a guard dog, but they are larger framed dogs, so< pending personality traits in the DOG itself may or may not have some drive there
ME personally I would NOT want a HUNTING dog to have ANY aggression in them due to while hunting your going to be running into far too many people, and or other animals, add in hiking and gets worse
a dog with aggression or more protection issue's can be a liability issue and a law suit wavering!
MOST all IMO GOOD hunting dogs are very laid back, relaxed and super friendly dogs, that get along with others and other dogs and animals
my last Lab, knew its owner had guns and as such, he was friendly to everything and everyone, NOT a mean bone in his body, and that was perfect to me!, anyone could pull food out of his mouth and he would never EVER growl or fight, no worries about him ever biting anyone! yet he hunted with a ton of passion, and was a as great a friend as anyone could ever ask for
hunted all types of game too, but was best at upland game,, pheasants being #1 and as I wanted it!
I personally would ask myself what animal I want to hunt MOST however and pick a do that does that best, and live with doing the rest IF so or not
get a second dog! or third dog if you need more specialized for species/guard duty!
and I sure hope you realize how much work is involved in training here, its a LOT and on many different levels, and species, your going to have to be making sure they got one down before moving on to next and then BACK again often so they stay on track of first and second species!
way more work than I am up for these days LOL