When I started training my puppy, I used dehydrated meat. It's real meat and could be compared to what the Honest Kitchen offers, except in convenient small treat portions. I bought them at PetSmart (in Canada) and they were reasonably priced given they weren't filled with junk! I think its nice to give something different than their usual meal because, well... its a treat
In my opinion, it is good to give your pup a treat for training purposes but I realized my dog was becoming dependent on the treat because I was giving her one every time she did a trick (meaning she would only want to do the trick if she knew she would get a treat) so I started, to give her treats every couple times she would do a trick and now she realizes she may or may not get one but she does the trick now just for praise! PRAISE, PRAISE, PRAISE! I find praise is even helpful when training them to go outside. I NEVER hit my dog when she had an accident and it has proven to be successful. If you hit a dog, they are more likely to hide and go (inside) and become sneaky because they fear getting in trouble - and too I think its mean! I never hit my dog, just would pick her up and run her outside every time she would squat and she learned quick. When she went outside I would praise her and give her a treat here and there. She picked up super quick!
As for the puppy food question, I fed my dog Bella Blue Buffalo Wilderness since she was a puppy up until about 6 months ago when I realized she developed an allergy. I've come to realize through this forum that Blue Buffalo is not a high quality food, unlike what they say. Although I am getting off track of your initial question, I wanted to throw that out there!!
From what I understand dogs don't really develop allergy symptoms until after 2, (my dog was 2 1/2). So just keep an eye out! The food I just recently switched to is Natural Balance limited ingredient and she seems to like it!
But back to your question, I mainly fed my dog kibble but on occasion would either mix the same brand of wet food in with kibble and for a BIG treat, just gave her wet food, no kibble. You have to make sure that when you mix food it is ok for your dog - If you decide on one brand, its safest I find to keep the wet food the same brand as the dog food to ensure your dog doesn't get sick! If you switch them cold turkey to another brand its more than likely going to make your dog sick!
Hope this helps!