Blimey, where to start?! It depends on what sort of dog you think you'd like to adopt - do you want a really young one or are you happy to take an older one (the latter are obviously the hardest for rescues to find homes for)? Are you hoping for a specific 'breed' or are you open? Large, medium or small?
The big rescue centres like Dogs Trust and RSPCA are often the hardest to engage with. We only adopt (we have rescue dog number 4 with us right now) from a small, volunteer-run charity as we know that the people who run it take no risks with dogs and only rehome them to people they've checked out well. They will not rehome a dog to inexperienced adopters if it has specific needs, traits, etc, for example. A lot of people get annoyed at rescues for not rehoming dogs to families with young children - but the 'good' rescues know that unless they know for certain a dog's 'provenance', they cannot take that risk.
The charity we adopt from is very, very honest if a dog has a history of abuse and behaviours arising from it. Good rescues also often ask that adopters do more than a simple 'meet and greet' - where possible, returning several times to form a bond with the dog and ensure they really are serious.
We've had three dogs (before current one) who were 'hard to rehome' dogs - two were large, older crossbreeds and one had a shocking history of cruelty and abuse which made her fearful of almost all humans (and other dogs). She formed an amazing bond with us, but we had to ensure other humans didn't put their hands near her head, as she'd been severely beaten in her previous life. She died of cancer last year and we still miss her!
But current dog came to us with full provenance, after her owner (who'd raised her from a puppy) died very suddenly and unexpectedly. As a result, she's a dream to own!
Have a look at small rescues (do look at the well-known ones too) but for any dog that you think might suit you, ask lots of questions about what they know about the dog's behaviour. Good rescues are very honest - simply because they don't want dogs returned to them (which further traumatises the dog).
Good luck!