@johngottfredson , in my opinion you have to be willing to upgrade the physical size of the dog to get out of the yappy, annoying characteristics. I'm sure there are some individual experiences with small or mini sized dogs that are mellow and chill but I haven't really seen it personally.
Again, as anecdotal evidence, I've found that the bigger the dog the more relaxed they will be.
What are you guys wanting out of a dog? I think you should try and think of what characteristics you want then try and match those to a breed. You can certainly just pick a dog from a picture but if you try to match a dog based on how you guys live I think you're likely to have better success. You've said you want a dog that doesn't shed but they tend to have higher grooming needs. Are you willing to either brush the dog regularly or pay to have it groomed? What if the dog HATES the brush? On the other side are you willing to deal with a little hair if it means you don't need to do the brushing as frequently? Like everything in life there are trade offs and you just need to figure out which ones you are willing to give a little on. I'm sure you have already done it but look into what the type of dog was breed to do. Thats going to shed light on general, overarching characteristics you can expect to see independent of individual personality.
As much as I love my dog I really don't know that I'd get another great dane. They are really fun and very mellow but having the space to put him in a vehicle and take him camping is a huge consideration. Before we had our son if wasn't a huge problem but we really haven't taken him out (anywhere in the car) since then.