Hi Trittrot, so sorry things didn't work out for you. As you may know, rescues vary quite considerably in how they match up dogs and clients. These range from a pound where you can pretty much stroll in, take your pick and walk out to more reputable charities with much more detailed processes.
There's two ends to this - the assessment of the client and the assessment of the dog. Both are equally important. The right dog for me might be a terrible match for you. Client assessment is usually done by some sort of questionannaire/screening plus a homecheck. This is where we find out about your experience, expectations, family composition, lifestyle etc. Sometimes very detailed questions can feel intrusive - for instance if a couple don't have children, it's common to ask about plans for DC. This isn't us being nosey, it really is about making sure that a dog placed with you would cope with small DC. Similarly if you already have one small DC, we'd ask about plans for more. Sadly, one of the most common reasons for relinquishment is either the arrival of a first baby/pregnancy or more frequently, the pressures of a second baby when there is a toddler.
With regard to the assessment of the dog, the gold standard is for the dog to have been in a foster home for a period of time. This allows an unparallleled opportunity to study the dog's behaviour in a domestic setting, how they interact with people, other dogs and potentially DC (depending on the foster home) and cats. For a first time adopter, I would always recommend a dog that has been fostered and carefully assessed rather than one from a kennel.
The only exceptions to this are ex racing greyhounds as usually when they come in, they have come from a very predictable (indeed, rigidly so) breeding and training programme, and very often their entire racing/training history is known. A much more predictable dog/background.
With our own dogs, the first two were matched to us after a homecheck. We went to the kennels to meet the first one, took him for a walk, liked him, and then went back and collected him. We trusted the rescue to pair us with the right dog. I think they made a good match - for instance he would not have suited a busy household with lots of DC, but for us he is perfect. For our second hound, a similar process but this time we wanted to make sure both got on OK. They did, so she came home with us. 
After that, all the other dogs have been fosters or "failed" fosters who arrived as fosters but never left. We lost two very much loved elderly dogs this year and currently have a household of four hounds - one of ours (that first dog) and three fosters.
Rescues will be OK if an adoption has previously gone wrong - it happens, even with careful screening. If you are ready to adopt again, and would like a recommendation for a good, reputable charity, please let us know or PM me, saying roughly where in the UK you are. Between the rescue peeps here, we can steer you to the best charities with the most thorough approaches.
Good luck. 