I think with rescues - they match you with what you are happy to take on, but obviously it’s easier to find fosterers for easier dogs, also they might not have a good assessment of them at that point, but I’m sure someone who does that could answer better.
With mine, they don’t take dogs under I think it’s a a year, or dog’s the owner has owned for less than a year as it’s unfair on the dog to spend what could be a fairly long time elsewhere and then go back
And they don’t take any with major behavioural issues - because they usually come straight from the owners house to yours. There’s background information as well, how much exercise they usually get, where they sleep, what they’re like with other dogs, the vet that sort of stuff and a list of commands they know.
I find it’s not accurate - usually not on purpose, I don’t think anyway, just things like owners put in a huge list of commands and the dog actually only responds to its name and sit, lol, but we’ve had no huge problems. They’ve all been really sweet, pretty well behaved dogs, no toileting issues or destructiveness or anything like that, just things they’re supposed to know they look a bit blankly at you or they’re not hugely social with other dogs when their owner says they like to play with them.
And yep, everything is paid for... food gets delivered, vets charge them direct and if I need anything for them, toys, treats, and extra kong or whatever I’m supposed to tell them and they’ll get it to me, but I do buy wee bits and pieces sometimes.