Good breeds for chicken protection, chipmunk hunting and loving

The missus and I are considering getting a dog.  We've recently lost some chickens to a fox.  We have an overabundance of chipmunks and ground squirrels in the garden.  It would be nice to have a warning when someone comes down the driveway.  Having a furry friend would also be nice.

But we'd rather not have a lot of mess and shedding.  I think a smaller dog would be better.  A friend has a "teddy bear" dog and it doesn't shed and is about the right size..

Is there a type of breed or range of breeds that might fit the bill?  Are most of those characteristics determined by training and encouragement?  I suspect just having any dog around the place might be enough to deter a fox but I'm not sure...

Lots of good dog breeds out there Mike and some fine (mutts as well).
Watch out for the "designer" dogs , steer clear of them for many reasons beyond the stupid prices they are asking.
Almost all will shed...   It seems to us that short hair dogs shed more than long coated ones.

Good luck finding the perfect puppy to chew up your good shoes... lol

Now to answer your question.
Myself I would steer clear of retriever dogs.
Wonderful nice dogs but they live for the ball!  As bad as a heroin junky.

LGD dogs would certainly protect your chicks and any kidlets you might have now or in the future...
Probably not going to care much about squirrels.     They can be  aggressive to strangers. (Not always a bad thing)

Terriers are good dogs and might go after your rodents for you.
There are numinous different "models" of terrier in all sizes.

Hunting dogs are great for hunting but not much else .
Heeler dogs are another working dog. I personally like them but they can be biters to strangers. (their great if you have cattle)

So many more to look at !   You're going to have a hard time.
I suggest  looking on line at different breeds and narrow down what you like .

Beware going to see puppy's  before picking what breed/ style your wanting!!!     At the pound or a privet sale .
They will grab your heart and you will end up coming home with a  pup that you will love and will love you but... might not do the other things you want.

My parents have a malshi - Maltese x shih tzu. It's basically a little white fluffball. He doesn't really shed, but he needs his hair trimmed regularly.

He goes absolutely nuts when there's a squirrel or coyote in the yard. The squirrels just shout back, but (so far) the coyotes have all made quick exits. He's small enough that an assertive chicken could probably deal with him if need be. I don't think he's much of a digger, though, what with the teeny tiny paws and all. So underground rodents would probably laugh at him.

A little dog like a dachshund, West Highland terrier, Rat terrier, or Scottie - trained right - would be great at getting rid of those crop stealing little fur balls, and I'm sure could hold their own against the fox - especially the latter three. But, since you have chickens, you'll have to be extra careful about bonding them with your birds.

I'm looking at ads every now and then and there are some decent "backyard mixes" which people advertise, and many times the parents are already used for a certain purpose (like hunting for small garden critters). So maybe keep an eye on local ads. It also gives me an idea which breeds are most popular in my area for this purpose. Currently, I have a sighthound and he doesn't hunt like that but even his presence seems to keep some critters away (definitely foxes and cats - he can't catch them because the garden is too cluttered for him to run fast enough, he's too big).