My favorite treats are Liver Biscotti: http://www.amazon.com/Liver-Biscotti-Whe...05705485&sr=8-3
Not cheap, but they are small crunchy bites that dogs love, and they don't need refrigeration or leave your hands icky. I use them a lot for nail trims.
Zukes Mini-Naturals: http://www.zukes.com/woof/mini-naturals.html
Very tiny soft pieces, perfect for puppy training, and they also don't need refrigeration. You can even pinch them into smaller bits with your fingernail to make them go further.
Natural Balance rolls: http://www.amazon.com/Natural-Balanc.../dp/B0002Y1QCU
Looks and smells like salami, but it's a nutritionally complete dog food. I've never known a dog who didn't love NB rolls. The only drawback is they do need refrigeration, so I usually toss my treat bag in the fridge when I'm done training, or put them inside a plastic bag that I can take out and refrigerate. You can easily cut up a roll into tiny (1/4") pieces and store them in a ziplock bag or plastic container in the fridge or freezer for later use.
Old Mother Hubbard biscuits: http://www.amazon.com/s?ie=UTF8&rh=n...Hubbard&page=1
They have small puppy sized biscuits, which are good to stuff in your pocket to reward pottying outside.
Solid Gold Jerky: http://www.onlynaturalpet.com/product_de...&click=124&mf=2
The pieces are too big if you're going to use a lot of treats, but they are easily broken up with your fingers as you go, or chopped up in advance.
Freeze dried liver is good too, but should also be cut up into much smaller pieces. People food treats I sometimes use are cheese and hotdogs, as long as your dog doesn't have any digestive issues. The commercial treats I listed above are all readily available, either in pet stores or online, and are have good healthy ingredients, unlike some of the cheaper products. No matter what you use, you should cut back on your puppy's food if you're going to use a lot of treats in training so he doesn't get too many calories.
If your pup is very food motivated you can use a portion of his daily kibble for training treats. For some dogs, especially in a very distracting environment such as a training class, that might not be motivating enough, but it might still be fine around the house. Cassidy would work for kibble at home, but needed something higher value in class. Keefer was on a special diet for a few months while he was being treated for SIBO and wasn't allowed any treats at all at a time that we were in a training class. Fortunately, he's so into food, all food, any food, that he worked very well for kibble even in class.