your lifestyle is the main concern when deciding whether to get a dog, choosing the dog comes next.
is your house suitable for a dog? i.e. is the garden secure?
will there be somebody at home for most of the day? dogs can't really be left alone for more than 4 hours. In the case of a puppy, they really need to be supervised all the time.
will the dog be taken for walks every day? most dogs need about an hours walk a day.
you said you can't afford a pedigree, will you be able to afford neutering, vaccinations etc. if the rescue hasn't done this already?
as for choosing a breed.....
any breed will be good with kids/other animals if they are trained and socialized properly with them.
if you get a puppy you'll need to get him out and about mixing with other dogs to prevent him having issues with them when he is older. puppy training classes are a good way of doing this or getting him to mix with friends/family/neighbours dogs etc.
some breeds that are renowned for their reliability around kids are staffies and greyhounds as they have such gentle temperaments. however staffies are very playful and strong so may accidentally knock a small child over.
but really, any breed/type of dog will be fine with kids, it all depends on the individual dog's temperament. If you go to a good rescue, they should be able to match you to a nice friendly reliable dog.
Good luck!