Hmm, I have a large house and a fairly large yard, but my fencing is not too high, I'd say 3-2 metres high. I'm currently still living with my parents and sister, we have 2 miniature dachshunds (ones paralysed, a cat, Guineapigs and 2 birds. I have had little experience with dogs but I've helped my mother take care of my paralysed dog, so this will be my first dog. I'd like a dog that doesn't shed too much a little to moderate is fine, for grooming sessions I'd like to keep it to once or on most twice a week. I do still go to school so on weeks days I'll be out for 6-7 hours but on weekends I'll be at home and mostly go out once or twice during the weekend.
The first place I usually suggest is the shelter for people who aren't really sure what they want. You're likely to find all sorts of dogs there, from high-energy to mellow, low energy couch potatoes. An adult would be a good pet for a first-time dog owner because they have a known temperament and you can get a pet to fit your needs exactly.
If you want a purebred puppy, I would suggest looking into Rat Terriers (fairly mellow for a terrier), a Cocker Spaniel (pretty friendly all around, medium energy, just go more companion/show lines than field), any number of small companion dogs (Bichons, Shi Tzus, Lhasa Apso, Maltese). You haven't really given a lot of information, so there's really quite a few that could fit at this point....No matter what you choose, research your breeder very well before making a purchase. Many breeders for these dog breeds are backyard breeders with unsavory breeding practices.
Best bet, just go out and meet dogs at dog shows, talk to their owners, talk with your local shelter. You sound uncertain of what exactly you want, so its best to expand your horizons!
Also remember that if you ever leave and go to school and can't bring the dog with you, you have to be sure your parents are okay with taking care of the dog. If you ever move to an apartment or something, you have to be aware of size, weight, and breed restrictions in rentals, and note it may be harder to find housing.
If you do not know anything about dogs, the last thing I recommend is a shelter dog because you do not know what baggage you will get (genetically and previous handling). A good breeder will KNOW their dogs and will give you support after the sale as well as help you decide what dog is best suited.
I USED to say "get a rescue" but after helping people with rescues who have never had a dog.. I do not say that anymore. I see people with hearts as big as gold.. with these dogs that are always going to be a large management problem that they got from a shelter because they felt sorry for the dog (and no other reason!). If you go the shelter route you have to be prepared to walk away.. a LOT.
Remember this as well if you go the shelter route. IF there is a purebred dog at the shelter, that dog probably did NOT come from a responsible breeder so you may run into temperament issues and the like.
I would suggest a small dog. Not sure the shedding requirement will be easily met but off hand I am thinking a Pug. Other breeds that come to mind are Papillon (may have higher energy) and Chihauhau (and that last can have huge nerve issues!). Pomeranian can be good too. You might also consider an older dog (retired breeding female, retired show dog and so forth) to keep the energy level down some. Puppies of any breed are energetic.
Not all shelter dogs have baggage....many were given up because their owners simply didn't want a dog anymore, or living situations changed, or something else that has absolutely nothing to do with the dog itself. Some certainly have temperament and behavioral issues, but going to a shelter or rescue that fosters their dogs in homes will give you a very good idea of their real temperament. I have seen far more stable, friendly, and all-around great companion animals come from shelters than I have seen animals with issues.