If you end up going a route of getting a purebred breed and starting breeder research, the offa.org is a good site to begin. You can find your interested breeds, get a list of genetic health conditions that should routinely be screened for in breeding to improve the breed and eliminate known problems, and then you can look up kennel names as well as the parent names of the dogs when you have it down to a specific litter. You can also look up siblings and relatives of those dogs as well, and scan through the health testing results to get a good overview of what they are producing. While you may only want a "pet" or "family" dog and this might seem like a lot, families deserve to have healthy pain-free pets! It is actually a big job being a sound, stable, trustworthy full time "pet" and health issues can get in the way of that.
Lots of great choices and breed suggestions in this thread too!
I am partial to my working line German Shepherds. One of the things I looked for in a breeder was versatility. Are they producing dogs that are out in the world doing a healthy variety of tasks and environments, or are they focused on ONLY producing one type of sport-dog for one type of situation? I chose someone who across the board had dogs in almost every area you can think of from SAR, herding, bitesports, therapy and service dogs, pet, agility, etc. I wanted flexibility and adaptability in my dogs, and that's exactly what I get from them!