I always suggest first time dog owners avoid herding, hunting and Terrier breeds. (That eliminates the Shepherd and Beagle.) Sorry, but these breeds typically have a few traits that require some training know-how and more time and patience than a busy family can usually spare.
And FWIW, having “lot’s of room to run” isn’t nearly as important as spending time with and training your dog. (Do be aware that training for some breeds can be a 2-3 year-long process.)
I’ve been a foster and involved in rescue for some time and I will go on record as saying exercise is important, but lack of socialization and training is the #1 reason dogs end up in shelters.
Having had both I won’t get into a debate either for or against purebreds or rescues. What I will suggest is a visit to the AKC (Google American Kennel Club) site where you can learn more about the history, health and temperament of the breeds you are considering, including the breed traits that you will encounter in a mixed breed.
For example, there you would learn that Boxers “were originally used for dog fighting and to run down and hold large game such as wild boar and bison until the hunter could arrive. The breed is known for standing up on its hind legs and batting at its opponent, appearing to box with its front paws.”
Hm. So yes, this breed has probably retained some of the genetic stamp that makes them more inclined to “jump up” on people and other animals. And if you get a mixed breed that has Boxer in it, that dog could very well have some of the classic Boxer traits … to some degree … or not.
This goes for health-related issues too. Many people think mixed breeds are healthier when in fact, they share the same likelihood of inheriting any of the health issues of the breeds in their genetic gene pool.
While purebreds typically share a couple of known genetic health issues, mixed breeds can develop any of the health issues from any of the breeds in it.
When learning about different breeds be sure to pay close attention to descriptive terms like: aloof, wary, determined, etc. While some people (like myself) may value these genetic traits or personality quirks, they are often meant to serve as a PC warning.
Determined may mean the inability to quit and no capacity to feel fear, regardless of the odds or consequences. Aloof may mean indifferent to affection or praise. Wary may mean bonds with one person and distrusts extended family and friends.
Independent may mean prone to flip you the furry finger and take charge. Don’t be swayed by cute or pretty pictures … all breeds have their pros and cons and some genetic traits will run very true to the classic breed standard.
So it helps to know the true standard for your breed, because while training can help diminish or control some traits, others will be more difficult to control. This is very true of certain heritable traits of some breeds more so than others.
Breeds I’ve raised: German Shepherd, Brittany Spaniel, Irish Setter, Afghan Hound, Doberman Pinscher, Australian Cattle Dog. The least number of dogs I’ve ever had at any one time: Three.
Cappy