I've been browsing the Battersea website and notice that on many (nearly all) they say "needs previous experience dealing with the breed / nervous dogs etc". Clearly, this is sensible and responsible but does it mean that people who've never had a dog before find it difficult to get a dog from a shelter?
We got our first dog from the RSPCA. I was a teenager at the time, don't remember any particular problems.
Perhaps contact the rehoming centre and tell them about yourself - they might be able to help with matching. We adopted our current girl that needed "an experienced owner", we'd never had a troubled dog before but I did a qualification in canine behaviour and a chat with their behaviourist convinced them we'd be a good match.
It's all theoretical at this stage. We have a three year old and a one year old so I would want to wait until the kids were a bit older.
Not a puppy, I'd be happy with an older dog. Ideally, I'd like the sort of sandy coloured or black with a white muzzle mongrel that you used to see in pubs in Brighton in the eighties and nineties. Sounds a bit random, I know, but I'm not terribly interested in many breeds (apart from greyhounds / lurchers - which are themselves mongrels).
Yes definitely better to wait until the children are older I think. A lot of rescues won't rehome to people with small children AFAIK.
It might be worth having a think about breeds rather than how your dog "looks", as you'll need to make sure your dog fits your lifestyle. Have a look at some breed rescues, too. Do you want to go for long hikes through the country? I'm fairly certain that wouldn't suit a greyhounds as they need short sprints. What sort of training are you planning on doing? Will you get involved in anything like agility or flyball? If not then rule out the high energy breeds like collies or they'll be bored. How much exercise will you be able to give the dog? different breeds usually have different requirements.
Of course, the advantage of going for a rescue is that you'll have a better idea of the individual dog's personality, rather than basing your choice on a "breed type", which doesn't always ring true.
I've never had a greyhound or lurcher but it does sound like that's the sort of breed you'd be looking at. Definitely sofa dogs I think (although my labs would never leave the sofa if I didn't make them!).
I think there's a thread on here for hound owners? Maybe go and have a chat to them for advice?