It really depends on you. If I was meeting a dog that I might adopt I would first make sure he was good with cats and other dogs and I know the breed(s) would fit my lifestyle. Then I would go in with him (shelters and rescues should let you go in a room or outside with the dog) and I would want him to get excited and wag his tail like nuts, I'd be fine and even happy if he jumped up a little. I would want a dog that would be willing to play and enjoys being petted. For me I like really excitable and playful people oriented dogs. When Max was young if you started getting playful with him he would do zoomies and play bow and grab a toy and run around. When it was down time I could sit there with him for an hour and he would not move. As soon as I stopped petting he turned to me and started wagging his tail and staring at me like "where are you going
" he would lay on his back exposing his belly. He thrived on attention. That is the kind of dog I like, like Labradors. The main thing many people dislike about labs are that they are annoying, Max would have been classified by those people as annoying, which is fine he probably was. I like that though.
Do you want a dog who want attention and will need more time with you or a more aloof dog. Go meet the dog, make sure he is alert ad healthy then start doing stuff with him. Try holding him (if he is of the right size for that) pet him, play with him (bring a tennis ball if you want a dog with ball drive). See how fast he clams down and if he would rather cuddle or play. Some dogs won't want to play some dogs won't want o be petted, especially right after playing.
A lot also depends on how much work you are willing to do with your dog. You could clap your hands and the dog cowers and is afraid. Some people have the time and patience to work with a fearful dog and some people don't. I personally want dogs with behavioral issues (probably not fear though, I'd be more willing to work with jumping up, digging, chewing etc. but not so much fear and barking though minor fear I could do, I don't want a dog who freaks out when there is thunder) I want dogs who don't have much training because I really like to train.
So think about what you want. An excitable dog, a laid back dog an independent dog or a clingy dog.
Tell us more about what you want and we can help you tell what behavior to look for that would suggest the dog is like that.