It depends on how much you are used to dogs and training and caring for them.
If not so familiar or experienced, avoid the high energy, very sharp, big working types that tend to be a lot of dog to handle. Most of the breeds mentioned so far - LOL. 'Out in the country' isn't a good place to turn a dog loose to 'give him some exercise' if he is a sharper more energetic type - dogs in rural need fences or something to keep them from wandering.
Another thing to look at is the dog's coat. A long haired - well - even some of the thicker coated short haired dogs - well - let's just say - ALL DOGS SHED to some extent. If you're fussy about house keeping, stick to a dog that sheds less and has shorter, less thick fur. Some people feel the 'groomed breeds' (like the Poodles and others that get clipped by a groomer) 'don't shed'.
Another thing to think of is size. A big dog eats more, tends to happily knock over knick knacks every time he wags his tail(your decorating habits will veer away from those low coffee tables pretty quick), and can rather inintentionally knock over little children - they can be especially goofy when they're puppies, and tend to have a long adolescence. A big dog seems so appealing and so good at protecting the family, but the fact is that just about any dog will let you know when things aren't quite right on the property, a dog doesn't have to be big to be a very useful family member. Big dogs eat more, they need more room in the car, they are deucedly difficult to pick up and get to the car to the vet when they're hurt, and they need more of everything - grooming, bathing, etc.
I'm assuming the dog will be in the house so fur, size etc is an issue - but too, it won't be tuned into protecting you if it isn't in the house - it will just bark at every bird and cat that passes by if it's sitting tied up outdoors with nothing else to do.
For smaller, not too intense-to-groom dogs, you might consider a Cairn Terrier, Border Terrier, a Havanese, Norfolk or Norwich Terrier, or a Clumber Spaniel. There are many much smaller dogs, too. Of the terriers, the Cairn and Border tend to be more mellow and less 'terrier-ish'.
For a really interesting family and farm dog that is protective and active, you might consider a German Pinscher. They're active and good watch dogs, with a temperament much like a Doberman, but smaller, about 17-20 inches, and still have the same short coat. I just saw one and the owner is over the moon about this dog.
The most popular and therefore easiest to get breeds in Cincinnatti, are Labrador Retriever, German Shepherd Dog, Golden Retriever, Yorkshire Terrier, and Boxer (in order from 1-5).
There's nothing bad about cross bred dogs or 'mutts', though it's harder to predict what sort of temperament and size they will have. Still, many people are confident they can train their dog and work with whatever temperament it has.
For those who want to help the community and help a dog, a rescue dog might be a good answer. Most breed clubs run rescues for unwanted dogs of their breed. It can be a great way to get a great dog. Then there are the humane societies and general rescue organizations that are doing their best to find new homes for all different breeds.
Here's the popularity list by AKC registrations (numbers are ranking for 2009 and then 2008) - less popular breeds aren't necessarily bad, but they can be harder to find and more costly
Retrievers (Lab) 1 1
Yorkshire Terriers 2 2
German Shepherd Dogs 3 5
Dachshunds 4 3
Shih Tzu 5 4
Beagles 6 7
Poodles 7 6
Retrievers (Golden) 8 9
Boxers 9 8
Bulldogs 10 13
Chihuahuas 11 10
Pomeranians 12 11
Miniature Schnauzers 13 12
Maltese 14 14
Pugs 15 15
Boston Terriers 16 16
Shetland Sheepdogs 17 18
Rottweilers 18 19
Spaniels (Cocker) 19 17
French Bulldogs 20 24
Cavalier King Charles Spaniels 21 21
