A natural bristle brush is fine for this. If the dog is scratching excessively or there are irritated area it should be seen by a vet. It may have inhalent or food allergies that can be treated. Check the skin frequently for parasites such as ticks and fleas. Ticks carry Lyme as well as other diseases that can be deadly.
Fleas can contribute to skin problems and carry tapeworm.
Frontline prevents both fleas and ticks and is easy to apply. This and other products for parasite control are available from your vet. Teeth should be brushed daily if possible. Providing safe chew toys will also help. You vet should check teeth at least yearly and can do a professional cleaning to help prevent tooth loss and disease.