Go online and look at all the different breeds that you are interested in and see what the good and not so good qualities are that are common with the breed.
One of the most important things to look for is energy level. If you are a low energy level person or family, you want to try and find a dog that also has low energy. Maybe in that case an older dog would be the right fit. It you are high energy and plan on spending a lot of time working and training your dog then look for a more high energy breed. If you plan to adopt from a shelter or rescue, which I think is great, spend some time with the dog you are interested in. Bring that dog outside and see how he/she reacts in the outside world. Play with the dog a bit and also, ask if you can see how he/she reacts around other dogs. Bring a few dogs outside and see how your dog interacts with them.