Training treats should have certain qualities. They should be very palatable, which usually means they need to be semi-moist. Training treats should not be too greasy as you may want to store them in a pocket, and a re-sealable bag is also particularly helpful with regard to ease of use. For training, you should consider getting scored or perforated treats as they're easier to cut into equal-sized pieces. There are some brands that have treats for the different life stages.
Most treats are appropriate for older dogs and puppies.
Although with older dogs, the caloric intake often must be monitored closely, as older dogs are typically less active. It is acceptable although they should contain fewer calories than standard biscuits and treats. Lite treats or biscuits, or very small treats are recommended. Table scraps are really not an appropriate treat. There are far too many things a dog should not eat, especially chocolate.