I'm a fosterer for a small independent rescue. I think that claricebeansmum might have given you the wrong impression of fostering - no decent rescue would ask you to care for a dog which they haven't assessed and which isn't child-friendly. The agreement is that you have the dog for an agreed period of time although rescue will take him back earlier if requested, you teach or remind him of what a home life is and the rescue pays all food and vet bills.
There are different types of fosterer - for a start, there are foster careers who are there for the rescue because the rescue they're caring for only uses foster homes as it doesn't have kennels. Then there are rescue kennels who are grateful for fosterers helping out with just some of their dogs. This might be because the dog needs training in a particular area (lead, recall or he might benefit from living in an agility-practising home), he may be an oldie, a pup who needs socialising and training or he may have a health condition. A fosterer may just be asked to help out in order to free up a rescue kennel space so that the rescue can take in yet another unfortunate dog who would otherwise be put to his death.
My foster boy comes from the latter kind of rescue. He's epileptic and wasn't at all happy in kennels and so came to me (abridged version!). His case is a bit different - he's a foster dog in name only really, he's been here for coming up a year as we none of us have been looking to rehome him. I adore him (long haired white GSD, pic on my profile) and the rescue, who are friends of mine too and for whom I volunteer, are happy that he stays for good. He's epileptic and so they want him under their vet's care, hence he's still a foster boy, and they still provide for him wrt medication and food.
Fostering can be for anything from a couple of weeks until the dog goes to a new home, just to remind him of how to adjust to family life again to longer term for an older, harder to home dog. That's something to discuss with rescue, depending on what YOU are willing and able to deal with. For example, one of my fellow fosterers who has teenaged girls at home and a visiting adult DD with a baby and has in the past year or so fostered a Labradoodle pup for about 3 weeks before pooch was homed and a Dobie cross for a period of several weeks, who she taught agility along with her own two dogs.
Many of rescue's dogs come, as mine does, from family homes as a result of anything from a change of working hours to divorce, redundancy, losing their home or even just the owner having a baby and not wanting the dog any more. 
Rescue will choose a foster dog for you in the same way in which they would home one... after meeting you and all your family in your home and assessing the dog and the situation. Quite simply, avoid any which won't..
You'll find that the big rescues won't allow someone with small children to foster but many of the smaller, independent rescues will decide each application individually so if you're interested don't give up at the first hurdle if one rescue says no, try another.
ALWAYS ensure that any rescue you deal with carries out sufficient checks on you and your foster dog for your own wellbeing and peace of mind and that the contract and understanding between you is clear, the dog is neutered, vaccinated and microchipped to the rescue and that full support is at the end of the phone and you should be fine.
If I can help more, please just shout.