Wow. What a hot topic!
I disagree with a lot of the people on here about online dogs. Not every breeder is a puppy mill. However, if I couldn't go in person at some point and check it out, I wouldn't buy the puppy.
My brother had to have a black English Mastiff. The only breeder he could find was in Tennessee (he lives in Colorado). He had the breeder send him pics of all the puppies they had (6), and my brother picked out his puppy. He then flew to Tennessee to make sure before he agreed to the purchase. Then, at 8 weeks old, he drove there to pick the puppy up.
I think this was crazy, but he's happy.
I found my Welsh Terrier (non-shedding) online, but the breeder was a 4 hour drive. I drove there to make sure that the breeder was okay and that the puppies looked good and healthy. We love our Welshie and couldn't be happier.
As far as shelter dogs go, I understand why everyone wants to support them, but, if you have specific needs in a dog, it's best to get a breed that fits your family. Great if you can find that dog in a shelter. I like the idea of a breed-specific rescue group. There were no Welsh Terriers available when we were looking, but we would have happily gone that route.
And, I agree that you should really do your research on breed types. Every single breed has some negatives. When we started researching, we had the silliest list of things that we needed out of a dog: non-shedding, non-barking, small but not too small, not white (had a white dog in the past, hated how dirty he looked), kid friendly, etc...... What we ended up getting fit all those characteristics, but I pay the price with grooming. Non-shedding dogs usually, but not always, need more grooming. If they don't naturally shed their hair, you get to cut it! In the case of my wire haired terrier, I have to hand strip his hair, but I get the benefit of a dog that doesn't shed, doesn't smell, and dries in about 10 minutes flat.
Good luck in your search. Do what's right for you and your family.