Unfortunately, I don't think there is any solution that will keep your home 100% dog hair free, but there are options to mitigate it.
Make sure to regularly groom your dog. I have a double coated, kinda fluffy herder mutt dog, and using an undercoat rake gets a ton of dead hair out every time I use it. I use the undercoat rake about once every two weeks, then just a regular brush the rest of the time to remove debris from the hair. A good bath also helps, followed by the blow dryer. My dog does not like blow driers, so I like to bathe him on especially windy (but warm) days and let him outside so the hair just naturally gets whipped out of his coat by the wind!
A high-quality diet also helps, along with a fish oil supplement that helps with my dog's allergies. His coat is typically very shiny and sleek.
I have the Shark Pro Lift-Away Vacuum, and I think it works very well on the hair. It has a hard floor attachment, as well as an upholstery and dusting attachment, which are help to get hair off of furniture and surfaces. Shark sells a pet-specific vacuum, too, which I think I want to get when my current one breaks down. I've had it for nearly 4 years now, though, and no signs of breaking!
I also have a Roomba, which helps keep the place looking decent between thorough vacuuming. It picks up wonderfully on my hard floors, and decently on carpet. It keeps gobs of hair from forming on the carpet, but I still need to vacuum the carpets with my big machine once in a while. Before the Roomba, I had dust bunnies of dog hair everywhere and gobs of hair on the carpet, but the Roomba has made me feel like I don't need to vacuum every 2 days. The level the Roomba cleans is 850 sq. ft. and typically gets everything, but sometimes misses spots or runs out of battery before it can finish.
My current Roomba just kind of wanders from place to place in our small upper level, which works, but we are moving to a larger home soon where the main floor is as large as our entire current house, (1700 sq. ft.). If you have a fairly large house, I would suggest purchasing one of the newer Roomba models that "maps" your house so that it can return to its station to charge and empty it's bin, then go out and finish cleaning. If my Roomba had to clean our entire house, I think the bin would be full before it was half finished!
If being hair free is really important to you, I would honestly purchase a Shark (which is half the price of that Dyson, by the way) and a robot vacuum for in-between cleaning. I'm a neat freak, too, and having a robot vacuum to keep things clean between thorough house cleanings is awesome and relieves stress because I don't have to look at giant dog hair dust bunnies.