My neighbour got a rescue from one of the ‘big five.’ She was lied to (either deliberately or by omission) about the dogs behavioural issues - it ended up biting her and she PTS about a week ago - and that’s not uncommon (the lying). People either lie to the rescue and the rescue doesn’t properly check, or the rescue lies.
On the other hand…My mum has a rescue from Spaniel Aid - beautiful little dog. They were totally honest about her issues (and god, there were a lot - reactive, bad with men, bad with kids, severe separation anxiety, digging, submission urination, shadow chasing) so at least my mum went into it with her eyes open.
Rescuing is a great thing to do but after seeing what my neighbour went through, and anecdotally what I’ve seen from others on mumsnet about big kennel rescues, I’d never go with a charity that wasn’t breed specific.
You should get one that lives in foster IMO - that way the fosterer can be 100% sure about the sort of behaviour a dog is likely to have. Dogs in kennels behaved very differently once you get them into a home.
I’d also add if you have cats, or young kids visiting etc, it’ll be hard to rescue - the big five in particular are so beyond fussy about who they give dogs to (ironic given how poor they are at being honest about dogs issues) - so you may have to be very patient.