Minimu recently asked someone else considering a dog a very good question - Why are you getting a dog? And also a supplementary question - what do you intend to do with the dog?
Your (and your family) lifestyle have such a huge impact. Have a think about these because they will drive what sort of dog will fit best with your family. Are you likely to be doing lots of outdoor activities with dog as a family? Things like CaniX, geocaching, orienteering, biking? Would you want to be involved with things like obedience and agility? Is your lifestyle madly social, with masses of travelling, or lots of parties, childrens sleepovers etc.? Are you planning to have more children? It's not rude asking this since many rescues find that the crunch time for a lot of dog owners is when a second baby comes along and they already have a toddler - coping with two LOs and a dog often becomes too much and the dog goes.
This is one of the reasons why rescues often won't home to families with DC under 5.
No rescue would rehome to you if you said dog was going to be in an outdoor kennel or run (with the possible exception of very specialist rescues dealing with some northern breeds, and gundogs, where a dog was going to an experienced home, with existing kennels, or a farm environment) - generally rescues are rehoming dogs who are going to be family pets and as such would be expected to live in the house with you.
Dogs Trust are highly reputable - they will ask you to think very carefully about your lifestyle and probably attend a short training course (half a day) on dog ownership. They (and all good rescues) will encourage you to take dog to obedience classes such as KC bronze award - would thoroughly endorse this. A nicely mannered dog is a pleasure to live with - that's one with reasonable recall, walks nicely on lead, will sit, stay and get in and out of car reasonably. As you are in a rural environment, bad dog manners can (rightly so) get your dog shot.
What you could also consider is finding out more about dog ownership. Pop along to some doggy events such as fun charity shows, Cani X events etc - many local rescues often hold things like regular dog walks, social events etc where you can go along and in a no pressure environment meet some of the dogs and ask lots of questions. Taking your time in this way also shows the rescue that you are a responsible committed dog owner who is trying to prepare thoroughly. Another thing to consider is becoming a foster home for a charity - this is lovely since food and vets bills are paid by the charity and you have the fun bits of giving the dog a nice home. This is an excellent way of seeing if dog ownership works for you as a family in your circumstances.
Finally, it's really important that all the adults are fully signed up to having a dog, and also that you've thought very hard and carefully about the financial side of dog ownership. Even with a healthy dog, insurance is vital, and there are a whole host of other costs to think about like regular worming, vaccinations, kennel fees if you go away, food etc.
Good luck! 