As far as rescues go, Dogs Trust is one of the most responsible IMO. I know there's debate about the never putting a healthy dog down, but at the rehoming end, they are very thorough. When we adopted from DT, they asked loads of questions, and made sure I was a suitable owner for our (then) very difficult dog. They checked our home and garden, spayed the bitch etc. Dogs Trust, as mentioned above, are also very good at education programmes. Our bitch had been through some therapy/training, even if we had a lot more work to do. And the DT kennels are clean and as stress free as possible for the situation.
Last week we got a dog from a local rescue. I know they are trying hard, but the place was disgusting and made my heart break. It stank, was filthy and every single dog was visibly highly stressed. We only went there because we'd been told about this particular dog who could be a good pairing (not for breeding, just company) with our difficult bitch. Once the dog was out of the kennel to meet us, I refused to put him back. They didn't put up a fight and let me take him that day, no questions asked (but money taken). He had not been neutered and for all they knew, we lived in tiny one-bed flat with no garden, not suitable for this big dog (part Newfoundland). What really annoyed me about that rescue was that it operates also as a boarding kennel (as if) and that they were breeding a particular breed as well.
Turns out our new dog had been taken to DT though, and they wouldn't accept him because he is chipped. Unfortunately, the owners he is registered to denied all knowledge. If only there was a law to make them responsible. He's a friendly big mutt, desperate to please us and his only fault so far has been an upset stomach. I just don't get why he was abandoned. When he's not being walked or having a quick play, he's curled up on my toes
Anyway, I strayed off point. The rescues all have their faults, but DT is, overall, a good one.