As an image is often easier to understand as a long text. Here we go
Before fights you can easily filter dragons but you can't do that for training. It would be good to have filters on rarity, elements at least. A useful option would be also All trainable dragons / Only trainable dragons that are not fully trainable (can we train again a dragon that has four trained attacks?) And finally a filter on the dragon Rank. "A" ranked dragon are the one I mostly use so they are almost trained whereas no ranked dragon are almost not trained and that's between them I would like to find dragons to train.