Best breeds for areas with predation problems?

So we have decided to get another flock of chickens this year. We have about 5 acres of woodland with some open areas that we like to let them roam around on. The big problem with this that we faced last time is predation. Weather it was hawks coming in the day time or raccoons coming at night to pick off the ones that roosted in the trees; we were losing 1 bird a week on average.

We still want to keep them free range, so I was just wondering if anyone had any suggestions about breeds that stand a better chance of survival against predators? I was thinking smaller, wilder looking(more camouflaged), better flying birds would be the best bet. Yet still we hope to get some decent egg production and the occasional stew meat bird... All suggestions appreciated!

Local backyard free-ranging birds are the best option.

We got a mix of kinds when we moved here. The banties are more often carried off by hawks and night-climbing predators but we still have a remnant. The two breeds that have done the best for us are the game birds (run-of-the mill fighting kinds) and the Easter Eggers we got from someone whose hen went broody. The Easter Eggers go broody 2-3 times a year, the game hens are known for viciously defending nest and offspring. The two breeds combined gives us a very smart, bird with excellent survival skills.

I've noticed that when a predator starts "hitting" them at one roost they'll move to another location. A skunk went in the barn and the next night about 6 of them were in the henhouse that I shut at night (the night before there was only one hen in the henhouse). The Easter Eggers try to roost in the garage and on the front porch preferentially - where the dogs are most likely to protect them from night prowlers. They're that smart! They also sleep with the pigs at night - not much will mess with the pigs!

You need LGDs, two would be best. My breed recommendations are Maremmas & Great Pyrenees. No, they don't eat any more than smaller dogs because they lay around most of the time, not using energy.

In my area there is such biodiversity that it doesn't matter what breed, chickens will not last free ranging.White chickens tend to go first.

The dogs do help! Mine has even learned to look up when the chickens give the warning "hawk" call, and he'll chase the hawks away.

This morning I found clumps of feathers across the lawn from a hen that had been caught and plucked by some predator. Then, amazingly I found the hen! Lost some dignity and most of her tail but she's alive and well. I can only guess the dogs heard the racket and got there in time to chase off whatever was trying to eat her!

My dog also keeps an eye out for foxes and runs them and stray dogs off whenever he spots them.

I probably couldn't have chickens free range without my dogs!

ETA: mine aren't LGD's - I have a heeler, who is the main guard dog, and then a Corgi X Jack Russell and a Cocker Spaniel X chihuahua. The Corgi mix is a puppy and is being trained by the heeler to guard the poultry.

I do think LGDs are better but there are a few dogs that would be really hard to keep with chickens. Any kind of "bird dog" for example. You'd be working against their natural inclinations.