I use Cheerios, boiled chicken breast (it's true that it's messy), and Merrick's dehydrated lamb lung fillets (it's easy to pinch off teeny tiny pieces without being messy)
https://www.amazon.com/Merrick-Texas.../dp/B00EDJCICW.
From my own experience, I'd caution against using treats heavy in liver (from any animal). Liver is very yummy to dogs, because it's very rich in nutrients. When fed too much (as you probably will during a training class), your puppy may end up with the runs. Mine did. It was so sad - Scottie got sick after each training class. The instructor got very irritated at us.
https://www.vetinfo.com/liver-treats-for-dogs.html
After several upset stomachs, I switched to lamb lung.
Just note that if fed too much of any treat though, they'll get upset stomach regardless.