I have to agree that his tail looks like it has been damaged in some way and he may be able to grow it back. I know that you are getting a bigger tank, but to your question of long or tall tank, goldfish need the room to swim, not the depth. I started fishkeeping with fantails. They are lovely to watch. Any floating plant will help with the water quality. Regular water changes - which you know because you have had extensive experience.
I miss mine, but I don't have the room to have a larger aquarium for them. I'm enjoying my tetras and cories in my 20 gallon